134 Integrals from Integral-Table.com

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• Int frac{x}{\sqrt{x\pm dx frac{2}{3}(x\mp 2a)\sqrt{x\pm
• Int sqrt{\frac{x}{a-x dx sqrt{x(a-x)}-a\tan^{-1}\frac{\sqrt{x(a-x)}}{x-a
• Int sqrt{\frac{x}{a+x dx sqrt{x(a+x)}-a\ln left sqrt{x sqrt{x+a}\right
• Int x sqrt{ax b dx frac{2}{15 a^2}(-2b^2+abx a^2
• X x^2 cos int dx left sin
• X^2 cos ax int dx frac{2 x a^2
• 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
• Int sqrt{x^3(ax+b dx 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 a\sqrt{x sqrt{a(ax+b
• Int\sqrt{x^2 pm a^2 dx frac{1}{2}x\sqrt{x^2\pm a^2}\pm\frac{1}{2}a^2 ln left
• Int sqrt{a^2 x^2 dx frac{1}{2 x sqrt{a^2-x^2}+\frac{1}{2}a^2\tan^{-1}\frac{x}{\sqrt{a^2-x^2
• Pm int x sqrt{x^2 a^2 dx frac{1}{3}\left x^2
• Pm int frac{1}{\sqrt{x^2 a^2 dx ln left x
• Int frac{1}{\sqrt{a^2 x^2 dx sin^{-1}\frac{x}{a
• Int frac{x}{\sqrt{x^2\pm a^2 dx sqrt{x^2 pm
• Int frac{x}{\sqrt{a^2-x^2 dx sqrt{a^2-x^2
• Int frac{1}{\sqrt{x\pm dx 2\sqrt{x\pm a
• Int frac{1}{\sqrt{a-x dx 2\sqrt{a-x
• Pm int frac{x^2}{\sqrt{x^2 a^2 dx frac{1}{2}x\sqrt{x^2 a^2}\mp frac{1}{2}a^2
• Int x\sqrt{x-a dx left\{\begin{array}{l}\frac{2 a}{3 left({x-a}\right)^{3/2 +\frac{2 5}\left
• Int sqrt{ax+b dx left(\frac{2b}{3a}+\frac{2x}{3}\right)\sqrt{ax+b
• Int ax+b)^{3/2 dx frac{2}{5a}(ax+b)^{5/2
• Int x^n dx frac{1}{n+1}x^{n+1},\hspace{1ex}n\neq 1
• Int frac{1}{x}dx ln |x|
• Int u dv uv v du
• Int frac{1}{ax+b}dx frac{1}{a ln |ax b|
• Int frac{1}{(x+a)^2}dx frac{1}{x+a
• Int x+a)^n dx frac{(x+a)^{n+1}}{n+1 n\ne
• Int x(x+a)^n dx frac{(x+a)^{n+1 n+1)x-a)}{(n+1)(n+2
• Int frac{1}{1+x^2}dx tan^{-1}x
• Int frac{1}{a^2+x^2}dx frac{1}{a}\tan^{-1}\frac{x}{a
• Int frac{x}{a^2+x^2}dx frac{1}{2}\ln|a^2+x^2|
• Int frac{x^2}{a^2+x^2}dx x-a\tan^{-1}\frac{x}{a
• Int frac{x^3}{a^2+x^2}dx frac{1}{2}x^2-\frac{1}{2}a^2\ln|a^2+x^2|
• Int frac{1}{ax^2+bx+c}dx frac{2}{\sqrt{4ac-b^2}}\tan^{-1}\frac{2ax+b}{\sqrt{4ac-b^2
• Int frac{1}{(x+a)(x+b)}dx frac{1}{b-a}\ln\frac{a+x}{b+x text a\ne b
• Int frac{x}{(x+a)^2}dx frac{a}{a+x}+\ln |a+x|
• 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
• Int sqrt{x-a dx frac{2}{3}(x-a)^{3/2
• B int sqrt{a x^2 x c dx frac{b+2ax}{4a}\sqrt{ax^2+bx+c}+\frac{4ac-b^2}{8a^{3/2}}\ln
• Int x sqrt{a x^2 bx c dx frac{1}{48a^{5/2}}\left
• Int\frac{1}{\sqrt{ax^2+bx+c dx frac{1}{\sqrt{a}}\ln left| 2ax+b sqrt{a(ax^2+bx+c
• Int frac{x}{\sqrt{ax^2+bx+c dx frac{1}{a}\sqrt{ax^2+bx c}-\frac{b}{2a^{3/2}}\ln left| 2ax+b sqrt{a(ax^2+bx+c
• Int\frac{dx}{(a^2+x^2)^{3/2 frac{x}{a^2\sqrt{a^2+x^2
• Ln int ax dx x
• X ln int dx frac{1}{2 x^2 x-\frac{x^2}{4
• Ln int x^2 x dx frac{1}{3 x^3 x-\frac{x^3}{9
• Int x^n ln x dx x^{n+1}\left dfrac{\ln x}{n+1}-\dfrac{1}{(n+1)^2}\right),\hspace{2ex
• Int frac{\ln ax}{x dx frac{1}{2}\left ln ax right)^2
• Int frac{\ln x}{x^2 dx frac{1}{x}-\frac{\ln x}{x
• Ln x int ax b dx left frac{b}{a
• Ln a^2 int x^2 hspace{.5ex dx x +2a\tan^{-1
• Ln a^2 int x^2 hspace{.5ex dx x +a\ln
• Left int ln ax^2 bx c\right dx frac{1}{a}\sqrt{4ac-b^2}\tan^{-1}\frac{2ax+b}{\sqrt{4ac-b^2}}-2x
• 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
• X^2 ln left int x a^2 b^2 dx
• Ln 2x x int x)^2 dx
• Ln x int x)^3 dx x+x x)^3-3 x)^2+6
• Ln x^2 int x x)^2 dx frac{x^2}{4}+\frac{1}{2 x)^2-\frac{1}{2
• Ln x^3 int x^2 x)^2 dx frac{2 x^3}{27}+\frac{1}{3
• Int e^{ax dx frac{1}{a}e^{ax
• Int sqrt{x e^{ax dx frac{1}{a}\sqrt{x}e^{ax}+\frac{i\sqrt{\pi}}{2a^{3/2}}\text{erf}\left(i\sqrt{ax}\right text erf}(x)=\frac{2}{\sqrt{\pi}}\int_0^x e^{-t^2}dt
• Int x e^x dx x-1
• Int x e^{ax dx left(\frac{x}{a}-\frac{1}{a^2}\right
• Int x^2 e^{x dx left(x^2 2x 2\right
• Int x^2 e^{ax dx left(\frac{x^2}{a}-\frac{2x}{a^2}+\frac{2}{a^3}\right
• Int x^3 e^{x dx left(x^3-3x^2 6x 6\right
• Int x^n e^{ax dx dfrac{x^n e^{ax}}{a dfrac{n}{a}\int x^{n-1}e^{ax}\hspace{1pt}\text{d}x
• Int x^n e^{ax dx frac{(-1)^n}{a^{n+1}}\gamma[1+n,-ax text gamma(a,x)=\int_x^{\infty t^{a-1}e^{-t}\hspace{2pt}\text{d}t
• Int e^{ax^2 dx frac{i\sqrt{\pi}}{2\sqrt{a}}\text{erf}\left(ix\sqrt{a}\right text erf}(x)=\frac{2}{\sqrt{\pi}}\int_0^x e^{-t^2}dt
• Int e^{-ax^2 dx frac{\sqrt{\pi}}{2\sqrt{a}}\text{erf}\left(x\sqrt{a}\right),\\\text erf}(x)=\frac{2}{\sqrt{\pi}}\int_0^x e^{-t^2}dt
• Int x e^{-ax^2 dx dfrac{1}{2a}e^{-ax^2
• Int x^2 e^{-ax^2 dx dfrac{1}{4}\sqrt{\dfrac{\pi}{a^3}}\text{erf}(x\sqrt{a dfrac{x}{2a}e^{-ax^2},\\\text erf}(x)=\frac{2}{\sqrt{\pi}}\int_0^x e^{-t^2}dt
• Int sin ax dx frac{1}{a cos
• Int sin^2 ax dx frac{x}{2 frac{\sin 2ax 4a
• Int sin^3 ax dx frac{3 cos ax}{4a frac{\cos
• Int sin^n ax dx frac{1}{a}{\cos hspace{2mm}{_2f_1}\left[\frac{1}{2 frac{1-n}{2 frac{3}{2
• Int cos ax dx frac{1}{a sin
• Int cos^2 ax dx frac{x}{2}+\frac sin 2ax}{4a
• Sin int cos^3 ax dx frac{3 ax}{4a}+\frac 3ax}{12a
• Int cos^p ax dx frac{1}{a(1+p)}{\cos^{1+p times{_2f_1}\left[\frac{1+p}{2 frac{1}{2 frac{3+p}{2
• Cos x int sin dx frac{1}{2}\sin^2 c_1 frac{1}{2
• Int cos ax sin bx dx frac{\cos[(a-b x]}{2(a-b
• Int sin^2 ax cos bx dx frac{\sin[(2a-b)x]}{4(2a-b)}+ frac{\sin
• Int sin^2 x cos dx frac{1}{3 sin^3
• Int cos^2 ax sin bx dx frac{\cos[(2a-b)x]}{4(2a-b frac{\cos
• Int cos^2 ax sin dx frac{1}{3a}\cos^3{ax
• 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
• Int sin^2 ax cos^2 dx frac{x}{8}-\frac{\sin 4ax}{32a
• Int tan ax dx frac{1}{a ln cos
• Int tan^2 ax dx x frac{1}{a tan
• Ax int tan^n dx frac{\tan^{n+1 a(1+n times{_2}f_1\left frac{n+1}{2},1
• Ax int tan^3 dx frac{1}{a ln cos frac{1}{2a}\sec^2
• X sec int dx ln tan tanh^{-1 left
• Int sec^2 ax dx frac{1}{a tan
• X sec tan int sec^3 dx frac{1}{2 frac{1}{2}\ln
• Sec int x tan dx
• Sec^2 int x tan dx frac{1}{2
• X sec^n int tan dx frac{1}{n n\ne
• Csc ln int x dx left tan frac{x}{2
• Int csc^2 ax dx frac{1}{a cot
• X csc int csc^3 dx frac{1}{2}\cot frac{1}{2 ln
• Int csc^nx cot x dx frac{1}{n}\csc^n n\ne
• X int sec csc dx ln tan
• X cos int dx sin
• Cos ax int x dx frac{1}{a^2 frac{x}{a sin
• Gamma(n+1 int x^n cos x dx frac{1}{2}(i)^{n+1}\left ix
• Int x^n cos ax dx frac{1}{2}(ia)^{1-n}\left 1)^n gamma(n+1
• X sin int dx cos
• Int x sin ax dx frac{x cos ax}{a
• Sin x int x^2 dx left(2-x^2\right cos
• Sin int x^2 ax dx frac{2-a^2x^2}{a^3}\cos +\frac x
• Int x^n sin x dx frac{1}{2}(i)^n\left gamma(n+1 ix
• X int cos^2 dx frac{x^2}{4}+\frac{1}{8}\cos 2x frac{1}{4 sin
• X int sin^2 dx frac{x^2}{4}-\frac{1}{8}\cos 2x frac{1}{4 sin
• X int tan^2 dx frac{x^2}{2 ln cos tan
• X int sec^2 dx ln cos tan
• X int e^x sin dx frac{1}{2}e^x cos
• Int e^{bx sin ax dx frac{1}{a^2+b^2}e^{bx b\sin a\cos
• Cos int e^x x dx frac{1}{2}e^x sin
• E^{bx cos ax int dx frac{1}{a^2 b^2 sin
• X sin int e^x dx frac{1}{2}e^x cos
• X cos sin int e^x dx frac{1}{2}e^x
• Int cosh ax dx frac{1}{a sinh
• Bx cosh int e^{ax dx begin{cases displaystyle{\frac{e^{ax}}{a^2-b^2 b
• Int sinh ax dx frac{1}{a cosh
• Bx sinh int e^{ax dx begin{cases} \displaystyle{\frac{e^{ax}}{a^2-b^2 b cosh
• Int tanh ax\hspace{1.5pt dx frac{1}{a ln cosh ax
• Int e^{ax tanh bx dx begin{cases}\displaystyle frac e^{(a+2b)x}}{(a+2b)}{_2f_1}\left
• Ax cos cosh int bx dx frac{1}{a^2 b^2
• Ax cos sinh int bx dx frac{1}{a^2 b^2
• Ax sin cosh bx int dx frac{1}{a^2 b^2
• Ax sin sinh bx int dx frac{1}{a^2 b^2
• Sinh ax int cosh dx frac{1}{4a}\left[-2ax 2ax
• Sinh cosh bx ax int dx frac{1}{b^2-a^2}\left[b

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