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integrals value
 i.e. $$\int e^x dx = e^x$$
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 Equation 0: $$\int x^n dx$$ $$\frac{1}{n+1}x^{n+1},\hspace{1ex}n\neq -1$$ $$\frac{1}{n-1}x^{n-1},\hspace{1ex}n\neq +1$$ Next Problem
 Equation 1: $$\int \frac{1}{x}dx$$ $$\log |x|$$ $$\ln |x|$$ Next Problem
 Equation 2: $$\int u dv$$ $$uv - \int v du$$ $$uv + \int v du$$ Next Problem
 Equation 3: $$\int \frac{1}{ax+b}dx$$ $$\frac{1}{a} \log |ax + b|$$ $$\frac{1}{a} \ln |ax + b|$$ Next Problem
 Equation 4: $$\int \frac{1}{(x+a)^2}dx$$ $$-\frac{1}{x+a}$$ $$\frac{1}{x-a}$$ Next Problem
 Equation 5: $$\int (x+a)^n dx$$ $$\frac{(x-a)^{n-1}}{n-1}, n\ne +1$$ $$\frac{(x+a)^{n+1}}{n+1}, n\ne -1$$ Next Problem
 Equation 6: $$\int x(x+a)^n dx$$ $$\frac{(x-a)^{n-1} ( (n-1)x+a)}{(n-1)(n-2)}$$ $$\frac{(x+a)^{n+1} ( (n+1)x-a)}{(n+1)(n+2)}$$ Next Problem
 Equation 7: $$\int \frac{1}{1+x^2}dx$$ $$\tan^{+1}x$$ $$\tan^{-1}x$$ Next Problem
 Equation 8: $$\int \frac{1}{a^2+x^2}dx$$ $$\frac{1}{a}\tan^{-1}\frac{x}{a}$$ $$\frac{1}{a}\tan^{+1}\frac{x}{a}$$ Next Problem
 Equation 9: $$\int \frac{x}{a^2+x^2}dx$$ $$\frac{1}{2}\ln|a^2+x^2|$$ $$\frac{1}{2}\ln|a^2-x^2|$$ Next Problem
 Equation 10: $$\int \frac{x^2}{a^2+x^2}dx$$ $$x-a\cos^{-1}\frac{x}{a}$$ $$x-a\tan^{-1}\frac{x}{a}$$ Next Problem
 Equation 11: $$\int \frac{x^3}{a^2+x^2}dx$$ $$\frac{1}{2}x^2+\frac{1}{2}a^2\ln|a^2-x^2|$$ $$\frac{1}{2}x^2-\frac{1}{2}a^2\ln|a^2+x^2|$$ Next Problem
 Equation 12: $$\int \frac{1}{ax^2+bx+c}dx$$ $$\frac{2}{\sqrt{4ac-b^2}}\tan^{-1}\frac{2ax+b}{\sqrt{4ac-b^2}}$$ $$\frac{2}{\sqrt{4ac-b^2}}\cos^{-1}\frac{2ax+b}{\sqrt{4ac-b^2}}$$ Next Problem
 Equation 13: $$\int \frac{1}{(x+a)(x+b)}dx$$ $$\frac{1}{b+a}\ln\frac{a-x}{b-x}, \text{ } a\ne b$$ $$\frac{1}{b-a}\ln\frac{a+x}{b+x}, \text{ } a\ne b$$ Next Problem
 Equation 14: $$\int \frac{x}{(x+a)^2}dx$$ $$\frac{a}{a+x}+\ln |a+x|$$ $$\frac{a}{a+x}+\log |a+x|$$ Next Problem
 Equation 15: $$\int \frac{x}{ax^2+bx+c}dx$$ $$\frac{1}{2a}\ln|ax^2+bx+c| -\frac{b}{a\sqrt{4ac-b^2}}\tan^{-1}\frac{2ax+b}{\sqrt{4ac-b^2}}$$ $$\frac{1}{3a}\ln|ax^3+bx+c| -\frac{b}{a\sqrt{4ac-b^3}}\tan^{-1}\frac{3ax+b}{\sqrt{4ac-b^3}}$$ Next Problem
 Equation 16: $$\int \sqrt{x-a}\ dx$$ $$\frac{2}{3}(x+a)^{3/2}$$ $$\frac{2}{3}(x-a)^{3/2}$$ Next Problem
 Equation 17: $$\int \frac{1}{\sqrt{x\pm a}}\ dx$$ $$3\sqrt{x\pm a}$$ $$2\sqrt{x\pm a}$$ Next Problem
 Equation 18: $$\int \sqrt{ax+b}\ dx$$ $$\left(\frac{2b}{3a}+\frac{2x}{3}\right)\sqrt{ax+b}$$ $$\left(\frac{2b}{3a}-\frac{2x}{3}\right)\sqrt{ax-b}$$ Next Problem
 Equation 19: $$\int (ax+b)^{3/2}\ dx$$ $$\frac{2}{5a}(ax+b)^{5/2}$$ $$\frac{2}{5a}(a^2x+b)^{5/2}$$ Next Problem
 Equation 20: $$\int \sqrt{\frac{x}{a-x}}\ dx$$ $$-\sqrt{x(a-x)} -a\tan^{-1}\frac{\sqrt{x(a-x)}}{x-a}$$ $$-\sqrt[3]{x(a-x)} -a\tan^{-1}\frac{\sqrt[3]{x(a-x)}}{x-a}$$ Next Problem
 Equation 21: $$\int \sqrt{\frac{x}{a+x}}\ dx$$ $$\sqrt[3]{x(a+x)} -a\ln \left [ \sqrt[3]{x} + \sqrt[3]{x+a}\right]$$ $$\sqrt{x(a+x)} -a\ln \left [ \sqrt{x} + \sqrt{x+a}\right]$$ Next Problem
 Equation 22: $$\int x \sqrt{ax + b}\ dx$$ $$\frac{2}{15 a^2}(+2b^2-abx - 3 a^2 x^2) \sqrt{ax-b}$$ $$\frac{2}{15 a^2}(-2b^2+abx + 3 a^2 x^2) \sqrt{ax+b}$$ Next Problem
 Equation 23: $$\int \sqrt{x(ax+b)}\ dx$$ $$\frac{1}{4a^{3/2}}\left[(2ax + b)\sqrt{ax(ax+b)} -b^2 \ln \left| a\sqrt{x} + \sqrt{a(ax+b)} \right| \right ]$$ $$\frac{1}{4a^{3/2}}\left[(2ax + b)\sqrt[3]{ax(ax+b)} -b^2 \ln \left| a\sqrt[3]{x} + \sqrt[3]{a(ax+b)} \right| \right ]$$ Next Problem
 Equation 24: $$\int \sqrt{x^3(ax+b)} \ dx$$ $$\left [ \frac{b}{13a}- \frac{b^3}{8a^3x}+ \frac{x}{2}\right] \sqrt{x^2(ax+b)} + \frac{b^2}{8a^{5/3}}\ln \left | a\sqrt{x} + \sqrt{a(ax+b)} \right |$$ $$\left [ \frac{b}{12a}- \frac{b^2}{8a^2x}+ \frac{x}{3}\right] \sqrt{x^3(ax+b)} + \frac{b^3}{8a^{5/2}}\ln \left | a\sqrt{x} + \sqrt{a(ax+b)} \right |$$ Next Problem
 Equation 25: $$\int\sqrt{x^2 \pm a^2}\ dx$$ $$\frac{1}{3}x\sqrt{x^3\pm a^3} \pm\frac{1}{3}a^3 \ln \left | x + \sqrt{x^3\pm a^3} \right |$$ $$\frac{1}{2}x\sqrt{x^2\pm a^2} \pm\frac{1}{2}a^2 \ln \left | x + \sqrt{x^2\pm a^2} \right |$$ Next Problem
 Equation 26: $$\int \sqrt{a^2 - x^2}\ dx$$ $$\frac{1}{2} x \sqrt{a^2-x^2} +\frac{1}{2}a^2\cos^{-1}\frac{x}{\sqrt{a^2-x^2}}$$ $$\frac{1}{2} x \sqrt{a^2-x^2} +\frac{1}{2}a^2\tan^{-1}\frac{x}{\sqrt{a^2-x^2}}$$ Next Problem
 Equation 27: $$\int x \sqrt{x^2 \pm a^2}\ dx$$ $$\frac{1}{2}\left ( x^3 \pm a^3 \right)^{2/3}$$ $$\frac{1}{3}\left ( x^2 \pm a^2 \right)^{3/2}$$ Next Problem
 Equation 28: $$\int \frac{1}{\sqrt{x^2 \pm a^2}}\ dx$$ $$\ln \left | x + \sqrt{x^3 \pm a^3} \right |$$ $$\ln \left | x + \sqrt{x^2 \pm a^2} \right |$$ Next Problem
 Equation 29: $$\int \frac{1}{\sqrt{a^2 - x^2}}\ dx$$ $$\cos^{-1}\frac{x}{a}$$ $$\sin^{-1}\frac{x}{a}$$ Next Problem
 Equation 30: $$\int \frac{x}{\sqrt{x^2\pm a^2}}\ dx$$ $$\sqrt{x^3 \pm a^3}$$ $$\sqrt{x^2 \pm a^2}$$ Next Problem
 Equation 31: $$\int \frac{x}{\sqrt{a^2-x^2}}\ dx$$ $$-\sqrt{a^2-x^2}$$ $$-\sqrt[3]{a^2-x^2}$$ Next Problem
 Equation 32: $$\int\frac{1}{\sqrt{ax^2+bx+c}}\ dx$$ $$\frac{1}{\sqrt{a}}\ln \left| 2ax-b - 2 \sqrt{a(ax^2-bx-c)} \right |$$ $$\frac{1}{\sqrt{a}}\ln \left| 2ax+b + 2 \sqrt{a(ax^2+bx+c)} \right |$$ Next Problem
 Equation 33: $$\int \ln ax\ dx$$ $$x \ln ax - x$$ $$x \ln a^2x - x$$ Next Problem
 Equation 34: $$\int x \ln x \ dx$$ $$\frac{1}{2} x^2 \ln x+\frac{x^2}{4}$$ $$\frac{1}{2} x^2 \ln x-\frac{x^2}{4}$$ Next Problem
 Equation 35: $$\int x^2 \ln x \ dx$$ $$\frac{1}{3} x^3 \ln x-\frac{x^3}{9}$$ $$\frac{1}{2} x^2 \ln x-\frac{x^2}{9}$$ Next Problem
 Equation 36: $$\int x^n \ln x\ dx$$ $$x^{n-1}\left( \dfrac{\ln x}{n-1}+\dfrac{1}{(n-1)^2}\right),\hspace{2ex} n\neq +1$$ $$x^{n+1}\left( \dfrac{\ln x}{n+1}-\dfrac{1}{(n+1)^2}\right),\hspace{2ex} n\neq -1$$ Next Problem
 Equation 37: $$\int \frac{\ln ax}{x}\ dx$$ $$\frac{1}{2}\left ( \log ax \right)^2$$ $$\frac{1}{2}\left ( \ln ax \right)^2$$ Next Problem
 Equation 38: $$\int \frac{\ln x}{x^2}\ dx$$ $$\frac{1}{x}+\frac{\ln x}{x}$$ $$-\frac{1}{x}-\frac{\ln x}{x}$$ Next Problem
 Equation 39: $$\int \ln (ax + b) \ dx$$ $$\left ( x - \frac{b}{a} \right) \ln (ax-b) + x , a\ne 0$$ $$\left ( x + \frac{b}{a} \right) \ln (ax+b) - x , a\ne 0$$ Next Problem
 Equation 40: $$\int \ln ( x^2 + a^2 )\hspace{.5ex} {dx}$$ $$x \ln (x^3 + a^3 ) +3a\tan^{-1} \frac{x}{a} - 3x$$ $$x \ln (x^2 + a^2 ) +2a\tan^{-1} \frac{x}{a} - 2x$$ Next Problem
 Equation 41: $$\int \ln ( x^2 - a^2 )\hspace{.5ex} {dx}$$ $$x \ln (x^2 - a^2 ) +a\ln \frac{x+a}{x-a} - 2x$$ $$x \ln (x^2 + a^2 ) -a\ln \frac{x-a}{x+a} + 2x$$ Next Problem
 Equation 42: $$\int \ln \left ( ax^2 + bx + c\right) \ dx$$ $$\frac{1}{a}\sqrt{4ac-b^2}\cos^{-1}\frac{2ax+b}{\sqrt{4ac-b^2}} -2x + \left( \frac{b}{2a}+x \right )\ln \left (ax^2+bx+c \right)$$ $$\frac{1}{a}\sqrt{4ac-b^2}\tan^{-1}\frac{2ax+b}{\sqrt{4ac-b^2}} -2x + \left( \frac{b}{2a}+x \right )\ln \left (ax^2+bx+c \right)$$ Next Problem
 Equation 43: $$\int x \ln (ax + b)\ dx$$ $$\frac{bx}{2a}-\frac{1}{4}x^2 +\frac{1}{2}\left(x^2-\frac{b^2}{a^2}\right)\ln (ax+b)$$ $$\frac{bx}{2a}-\frac{1}{4}x^2 +\frac{1}{2}\left(x^2-\frac{b^2}{a^2}\right)\ln (a^2x+b)$$ Next Problem
 Equation 44: $$\int x \ln \left ( a^2 - b^2 x^2 \right )\ dx$$ $$-\frac{1}{2}x^2+ \frac{1}{2}\left( x^2 - \frac{a^2}{b^2} \right ) \ln \left (a^2 -b^2 x^2 \right)$$ $$-\frac{1}{3}x^3+ \frac{1}{3}\left( x^3 - \frac{a^3}{b^3} \right ) \ln \left (a^3 -b^3 x^3 \right)$$ Next Problem
 Equation 45: $$\int (\ln x)^2\ dx$$ $$2x - 2x \log x + x (\log x)^2$$ $$2x - 2x \ln x + x (\ln x)^2$$ Next Problem
 Equation 46: $$\int (\ln x)^3\ dx$$ $$6 x-x (\ln x)^3+3 x (\ln x)^2-6 x \ln x$$ $$-6 x+x (\ln x)^3-3 x (\ln x)^2+6 x \ln x$$ Next Problem
 Equation 47: $$\int x (\ln x)^2\ dx$$ $$\frac{x^2}{4}+\frac{1}{2} x^2 (\ln x)^2-\frac{1}{2} x^2 \ln x$$ $$\frac{x^2}{4}-\frac{1}{2} x^2 (\ln x)^2+\frac{1}{2} x^2 \ln x$$ Next Problem
 Equation 48: $$\int x^2 (\ln x)^2\ dx$$ $$\frac{3 x^2}{37}+\frac{1}{2} x^2 (\ln x)^3-\frac{3}{9} x^2 \ln x$$ $$\frac{2 x^3}{27}+\frac{1}{3} x^3 (\ln x)^2-\frac{2}{9} x^3 \ln x$$ Next Problem
 Equation 49: $$\int e^{ax}\ dx$$ $$\frac{1}{a}e^{a^2x}$$ $$\frac{1}{a}e^{ax}$$ Next Problem
 Equation 50: $$\int x e^x\ dx$$ $$(x-1) e^x$$ $$(x+1) e^x$$ Next Problem
 Equation 51: $$\int x e^{ax}\ dx$$ $$\left(\frac{x}{a}-\frac{1}{a^3}\right) e^{ax}$$ $$\left(\frac{x}{a}-\frac{1}{a^2}\right) e^{ax}$$ Next Problem
 Equation 52: $$\int x^2 e^{x}\ dx$$ $$\left(x^3 - 3x + 3\right) e^{x}$$ $$\left(x^2 - 2x + 2\right) e^{x}$$ Next Problem
 Equation 53: $$\int x^2 e^{ax}\ dx$$ $$\left(\frac{x^2}{a}+\frac{2x}{a^2}-\frac{2}{a^3}\right) e^{ax}$$ $$\left(\frac{x^2}{a}-\frac{2x}{a^2}+\frac{2}{a^3}\right) e^{ax}$$ Next Problem
 Equation 54: $$\int x^3 e^{x}\ dx$$ $$\left(x^2-2x^3 + 6x - 6\right) e^{x}$$ $$\left(x^3-3x^2 + 6x - 6\right) e^{x}$$ Next Problem
 Equation 55: $$\int \sin ax \ dx$$ $$-\frac{1}{a} \cos ax$$ $$-\frac{1}{a} \sin ax$$ Next Problem
 Equation 56: $$\int \sin^2 ax\ dx$$ $$\frac{x}{2} - \frac{\sin 2a^2x} {4a}$$ $$\frac{x}{2} - \frac{\sin 2ax} {4a}$$ Next Problem
 Equation 57: $$\int \sin^3 ax \ dx$$ $$-\frac{3 \cos a^2x}{4a} + \frac{\cos 3a^2x} {12a}$$ $$-\frac{3 \cos ax}{4a} + \frac{\cos 3ax} {12a}$$ Next Problem
 Equation 58: $$\int \sin^n ax \ dx$$ $$-\frac{1}{a}{\cos ax} \hspace{2mm}{_2F_1}\left[ \frac{1}{2}, \frac{1-n}{2}, \frac{3}{2}, \cos^2 ax \right]$$ $$-\frac{1}{a}{\sin ax} \hspace{2mm}{_2F_1}\left[ \frac{1}{2}, \frac{1-n}{2}, \frac{3}{2}, \sin^2 ax \right]$$ Next Problem
 Equation 59: $$\int \cos ax\ dx$$ $$\frac{1}{a} \sin ax$$ $$\frac{1}{a} \sin a^2x$$ Next Problem
 Equation 60: $$\int \cos^2 ax\ dx$$ $$\frac{x}{2}+\frac{ \sin 2ax}{4a}$$ $$\frac{x}{2}+\frac{ \cos 2ax}{4a}$$ Next Problem
 Equation 61: $$\int \cos^3 ax dx$$ $$\frac{3 \sin a^2x}{4a}+\frac{ \sin 3a^2x}{12a}$$ $$\frac{3 \sin ax}{4a}+\frac{ \sin 3ax}{12a}$$ Next Problem
 Equation 62: $$\int \cos^p ax dx$$ $$-\frac{1}{a(1+p)}{\sin^{1+p} ax} \times {_2F_1}\left[ \frac{1+p}{2}, \frac{1}{2}, \frac{3+p}{2}, \sin^2 ax \right]$$ $$-\frac{1}{a(1+p)}{\cos^{1+p} ax} \times {_2F_1}\left[ \frac{1+p}{2}, \frac{1}{2}, \frac{3+p}{2}, \cos^2 ax \right]$$ Next Problem
 Equation 63: $$\int \cos ax \sin bx\ dx$$ $$\frac{\cos[(a-b) x]}{2(a-b)} - \frac{\cos[(a+b)x]}{2(a+b)} , a\ne b$$ $$\frac{\tan[(a-b) x]}{2(a-b)} - \frac{\tan[(a+b)x]}{2(a+b)} , a\ne b$$ Next Problem
 Equation 64: $$\int \sin^2 ax \cos bx\ dx$$ $$-\frac{\sin[(3a-b)x]}{4(3a-b)} + \frac{\sin bx}{3b} - \frac{\sin[(3a+b)x]}{4(3a+b)}$$ $$-\frac{\sin[(2a-b)x]}{4(2a-b)} + \frac{\sin bx}{2b} - \frac{\sin[(2a+b)x]}{4(2a+b)}$$ Next Problem
 Equation 65: $$\int \sin^2 x \cos x\ dx$$ $$\frac{1}{3} \sin^3 x$$ $$\frac{1}{2} \sin^2 x$$ Next Problem
 Equation 66: $$\int \cos^2 ax \sin bx\ dx$$ $$\frac{\cos[(2a+b)x]}{4(2a+b)} + \frac{\cos bx}{2b} + \frac{\cos[(2a-b)x]}{4(2a-b)}$$ $$\frac{\cos[(2a-b)x]}{4(2a-b)} - \frac{\cos bx}{2b} - \frac{\cos[(2a+b)x]}{4(2a+b)}$$ Next Problem
 Equation 67: $$\int \cos^2 ax \sin ax\ dx$$ $$-\frac{1}{3a}\cos^3{ax}$$ $$\frac{1}{3a}\cos^3{ax}$$ Next Problem
 Equation 68: $$\int \sin^2 ax \cos^2 bx dx$$ $$\frac{x}{4} -\frac{\sin 2ax}{8a}- \frac{\sin[2(a-b)x]}{16(a-b)} +\frac{\sin 2bx}{8b}- \frac{\sin[2(a+b)x]}{16(a+b)}$$ $$\frac{x}{4} -\frac{\sin 3ax}{8a}- \frac{\sin[3(a-b)x]}{16(a-b)} +\frac{\sin 3bx}{8b}- \frac{\sin[3(a+b)x]}{16(a+b)}$$ Next Problem
 Equation 69: $$\int \sin^2 ax \cos^2 ax\ dx$$ $$\frac{x}{8}-\frac{\sin 4ax}{32a}$$ $$\frac{x}{8}-\frac{\cos 4ax}{32a}$$ Next Problem
 Equation 70: $$\int \tan ax\ dx$$ $$-\frac{1}{a} \log \cos ax$$ $$-\frac{1}{a} \ln \cos ax$$ Next Problem
 Equation 71: $$\int \tan^2 ax\ dx$$ $$-x + \frac{1}{a} \tan ax$$ $$-x + \frac{1}{a} \cos ax$$ Next Problem
 Equation 72: $$\int \tan^n ax\ dx$$ $$\frac{\tan^{n+1} ax }{a(1+n)} \times {_2}F_1\left( \frac{n+1}{2}, 1, \frac{n+3}{2}, -\tan^2 ax \right)$$ $$\frac{\tan^{n+1} a^2x }{a(1+n)} \times {_2}F_1\left( \frac{n+1}{2}, 1, \frac{n+3}{2}, -\tan^2 a^2x \right)$$ Next Problem
 Equation 73: $$\int \tan^3 ax dx$$ $$\frac{1}{a} \ln \cos ax + \frac{1}{2a}\sec^2 ax$$ $$\frac{1}{a} \ln \sin ax + \frac{1}{2a}\sec^2 ax$$ Next Problem
 Equation 74: $$\int \sec x \ dx$$ $$\ln | \sec x + \tan x | = 2 \tanh^{-1} \left (\tan \frac{x}{2} \right)$$ $$\ln | \sec x - \tan x | = 2 \tanh^{+1} \left (\tan \frac{x}{2} \right)$$ Next Problem
 Equation 75: $$\int \sec^2 ax\ dx$$ $$\frac{1}{a} \tan a^2x$$ $$\frac{1}{a} \tan ax$$ Next Problem
 Equation 76: $$\int \sec x \tan x\ dx$$ $$\sec x$$ $$\csc x$$ Next Problem
 Equation 77: $$\int \sec^2 x \tan x\ dx$$ $$\frac{1}{3} \sec^3 x$$ $$\frac{1}{2} \sec^2 x$$ Next Problem
 Equation 78: $$\int \sec^n x \tan x \ dx$$ $$\frac{1}{n} \sec^n x , n\ne 0$$ $$\frac{1}{n} \csc^n x , n\ne 0$$ Next Problem
 Equation 79: $$\int \csc x\ dx$$ $$\ln \left | \tan \frac{x}{2} \right| = \ln | \csc x + \cot x| - C$$ $$\ln \left | \tan \frac{x}{2} \right| = \ln | \csc x - \cot x| + C$$ Next Problem
 Equation 80: $$\int \csc^2 ax\ dx$$ $$\frac{1}{a} \cot ax$$ $$-\frac{1}{a} \cot ax$$ Next Problem
 Equation 81: $$\int \csc^3 x\ dx$$ $$-\frac{1}{2}\cot x \csc x + \frac{1}{2} \ln | \csc x - \cot x |$$ $$-\frac{1}{3}\cot x \csc x + \frac{1}{3} \ln | \csc x - \cot x |$$ Next Problem
 Equation 82: $$\int \csc^nx \cot x\ dx$$ $$-\frac{1}{n}\csc^n x, n\ne 0$$ $$-\frac{1}{n}\sec^n x, n\ne 0$$ Next Problem
 Equation 83: $$\int \sec x \csc x \ dx$$ $$\ln | \tan x |$$ $$\log | \tan x |$$ Next Problem
 Equation 84: $$\int x \cos x \ dx$$ $$\tan x + x \sin x$$ $$\cos x + x \sin x$$ Next Problem
 Equation 85: $$\int x \cos ax \ dx$$ $$\frac{1}{a^3} \cos ax + \frac{x}{a} \sin ax$$ $$\frac{1}{a^2} \cos ax + \frac{x}{a} \sin ax$$ Next Problem
 Equation 86: $$\int x^2 \cos x \ dx$$ $$2 x \cos x - \left ( x^2 + 2 \right ) \sin x$$ $$2 x \cos x + \left ( x^2 - 2 \right ) \sin x$$ Next Problem
 Equation 87: $$\int x^2 \cos ax \ dx$$ $$\frac{3 x \cos ax }{a^3} + \frac{ a^3 x^3 - 3 }{a^2} \sin ax$$ $$\frac{2 x \cos ax }{a^2} + \frac{ a^2 x^2 - 2 }{a^3} \sin ax$$ Next Problem
 Equation 88: $$\int x^n \cos x dx$$ $$\frac{1}{2}(i)^{n-1}\left [ \Gamma(n-1, +ix) % \right . \nonumber \\ & \left . - (+1)^n \Gamma(n-1, ix)\right]$$ $$-\frac{1}{2}(i)^{n+1}\left [ \Gamma(n+1, -ix) % \right . \nonumber \\ & \left . + (-1)^n \Gamma(n+1, ix)\right]$$ Next Problem
 Equation 89: $$\int x^n \cos ax \ dx$$ $$\frac{1}{2}(ia)^{1-n}\left [ (-1)^n \Gamma(n+1, -iax) % \right. \nonumber \\ & \left. -\Gamma(n+1, ixa)\right]$$ $$\frac{1}{2}(ia)^{1+n}\left [ (+1)^n \Gamma(n-1, +iax) % \right. \nonumber \\ & \left. +\Gamma(n-1, ixa)\right]$$ Next Problem
 Equation 90: $$\int x \sin x\ dx$$ $$-x \cos x + \sin x$$ $$x \cos x - \sin x$$ Next Problem
 Equation 91: $$\int x \sin ax\ dx$$ $$-\frac{x \cos ax}{a} + \frac{\sin ax}{a^2}$$ $$-\frac{x \sin ax}{a} + \frac{\cos ax}{a^2}$$ Next Problem
 Equation 92: $$\int x^2 \sin x\ dx$$ $$\left(2-x^2\right) \cos x + 2 x \sin x$$ $$\left(2-x^2\right) \sin x + 2 x \cos x$$ Next Problem
 Equation 93: $$\int x^2 \sin ax\ dx$$ $$\frac{2-a^2x^2}{a^3}\sin ax +\frac{ 2 x \cos ax}{a^2}$$ $$\frac{2-a^2x^2}{a^3}\cos ax +\frac{ 2 x \sin ax}{a^2}$$ Next Problem
 Equation 94: $$\int x \cos^2 x \ dx$$ $$\frac{x^2}{4}+\frac{1}{8}\cos 2x + \frac{1}{4} x \sin 2x$$ $$\frac{x^2}{4}+\frac{1}{8}\sin 2x + \frac{1}{4} x \cos 2x$$ Next Problem
 Equation 95: $$\int x \sin^2 x \ dx$$ $$\frac{x^2}{4}-\frac{1}{8}\cos 2x - \frac{1}{4} x \sin 2x$$ $$\frac{x^3}{4}-\frac{1}{8}\cos 3x - \frac{1}{4} x \sin 3x$$ Next Problem
 Equation 96: $$\int x \tan^2 x \ dx$$ $$-\frac{x^2}{2} + \log \cos x + x \tan x$$ $$-\frac{x^2}{2} + \ln \cos x + x \tan x$$ Next Problem
 Equation 97: $$\int x \sec^2 x \ dx$$ $$\log \cos x + x \tan x$$ $$\ln \cos x + x \tan x$$ Next Problem
 Equation 98: $$\int e^x \sin x \ dx$$ $$\frac{1}{2}e^x (\sin x - \cos x)$$ $$\frac{1}{3}e^x (\sin x - \cos x)$$ Next Problem
 Equation 99: $$\int e^x \cos x\ dx$$ $$\frac{1}{2}e^x (\sin x + \cos x)$$ $$\frac{1}{2}e^x (\sin x - \cos x)$$ Next Problem
 Equation 100: $$\int e^{bx} \cos ax\ dx$$ $$\frac{1}{a^2 + b^2} e^{bx} ( a \sin a^2x + b \cos a^2x )$$ $$\frac{1}{a^2 + b^2} e^{bx} ( a \sin ax + b \cos ax )$$ Next Problem
 Equation 101: $$\int x e^x \sin x\ dx$$ $$\frac{1}{3}e^x (\cos x - x \cos x + x \sin x)$$ $$\frac{1}{2}e^x (\cos x - x \cos x + x \sin x)$$ Next Problem
 Equation 102: $$\int x e^x \cos x\ dx$$ $$\frac{1}{2}e^x (x \sin x - \cos x + x \cos x)$$ $$\frac{1}{2}e^x (x \cos x - \sin x + x \sin x)$$ Next Problem
 Equation 103: $$\int \cosh ax\ dx$$ $$\frac{1}{a} \sinh ax$$ $$\frac{1}{a} \cosh ax$$ Next Problem
 Equation 104: $$\int e^{ax} \cosh bx \ dx$$ $$\begin{cases} \displaystyle{\frac{e^{ax}}{a^2-b^2} }[ a \sinh bx - b \cosh bx ] & a\ne b \\ \displaystyle{\frac{e^{2ax}}{4a} + \frac{x}{2}} & a = b \end{cases}$$ $$\begin{cases} \displaystyle{\frac{e^{ax}}{a^2-b^2} }[ a \cosh bx - b \sinh bx ] & a\ne b \\ \displaystyle{\frac{e^{2ax}}{4a} + \frac{x}{2}} & a = b \end{cases}$$ Next Problem
 Equation 105: $$\int \sinh ax\ dx$$ $$\frac{1}{a} \tanh ax$$ $$\frac{1}{a} \cosh ax$$ Next Problem
 Equation 106: $$\int e^{ax} \sinh bx \ dx$$ $$\begin{cases} \displaystyle{\frac{e^{ax}}{a^2+b^2} }[ +b \cosh bx - a \sinh bx ] & a\ne b \\ \displaystyle{\frac{e^{2ax}}{4a} + \frac{x}{2}} & a = b \end{cases}$$ $$\begin{cases} \displaystyle{\frac{e^{ax}}{a^2-b^2} }[ -b \cosh bx + a \sinh bx ] & a\ne b \\ \displaystyle{\frac{e^{2ax}}{4a} - \frac{x}{2}} & a = b \end{cases}$$ Next Problem
 Equation 107: $$\int \cos ax \cosh bx\ dx$$ $$\frac{1}{a^2 + b^2} \left[ a \sin a^2x \cosh bx + b \cos a^2x \sinh bx \right]$$ $$\frac{1}{a^2 + b^2} \left[ a \sin ax \cosh bx + b \cos ax \sinh bx \right]$$ Next Problem
 Equation 108: $$\int \cos ax \sinh bx\ dx$$ $$\frac{1}{a^2 + b^2} \left[ b \cos a^2x \cosh bx + a \sin a^2x \sinh bx \right]$$ $$\frac{1}{a^2 + b^2} \left[ b \cos ax \cosh bx + a \sin ax \sinh bx \right]$$ Next Problem
 Equation 109: $$\int \sin ax \cosh bx \ dx$$ $$\frac{1}{a^2 + b^2} \left[ -a \cos ax \cosh bx + b \sin ax \sinh bx \right]$$ $$\frac{1}{a^3 + b^3} \left[ -a \cos ax \cosh bx + b \sin ax \sinh bx \right]$$ Next Problem
 Equation 110: $$\int \sin ax \sinh bx \ dx$$ $$\frac{1}{a^2 + b^2} \left[ b \tanh bx \sin ax - a \tan ax \sinh bx \right]$$ $$\frac{1}{a^2 + b^2} \left[ b \cosh bx \sin ax - a \cos ax \sinh bx \right]$$ Next Problem
 Equation 111: $$\int \sinh ax \cosh ax dx$$ $$\frac{1}{4a}\left[ -2a^2x + \sinh 2a^2x \right]$$ $$\frac{1}{4a}\left[ -2ax + \sinh 2ax \right]$$ Next Problem
 Equation 112: $$\int \sinh ax \cosh bx \ dx$$ $$\frac{1}{b^2-a^2}\left[ b \sinh bx \cosh ax - a \sinh ax \cosh bx \right]$$ $$\frac{1}{b^2-a^2}\left[ b \cosh bx \sinh ax - a \cosh ax \sinh bx \right]$$ Next Problem