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Calculus Integrals

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StarStarStarStar

dxx2+1\int \frac{dx}{\sqrt{x^2 + 1}}

StarStarStarStar

arsinh(x)+C\text{arsinh}(x) + C

StarStarStarStar

csc(x)dx\int \csc(x) \, dx

StarStarStarStar

lncsc(x)+cot(x)+C-\ln|\csc(x) + \cot(x)| + C

StarStarStarStar

1cos2(x)dx\int \frac{1}{\cos^2(x)} \, dx

StarStarStarStar

tan(x)+C\tan(x) + C

StarStarStarStar

arctan(x)dx\int \arctan(x) \, dx

StarStarStarStar

xarctan(x)12ln(1+x2)+Cx \arctan(x) - \frac{1}{2} \ln(1+x^2) + C

StarStarStarStar

xcos(x)dx\int x \cos(x) \, dx

StarStarStarStar

xsin(x)+cos(x)+Cx \sin(x) + \cos(x) + C

StarStarStarStar

exdx\int e^x \, dx

StarStarStarStar

ex+Ce^x + C

StarStarStarStar

11xdx\int \frac{1}{1 - x} \, dx

StarStarStarStar

ln(1x)+C-\ln(|1 - x|) + C

StarStarStarStar

ln(x)2dx\int \ln(x)^2 \, dx

StarStarStarStar

xln(x)22xln(x)+2x+Cx\ln(x)^2 - 2x\ln(x) + 2x + C

StarStarStarStar

cosh2(x)dx\int \cosh^2(x) \, dx

StarStarStarStar

14(sinh(2x)+2x)+C\frac{1}{4}(\sinh(2x) + 2x) + C

StarStarStarStar

x3dx\int x^3 \, dx

StarStarStarStar

14x4+C\frac{1}{4}x^4 + C

StarStarStarStar

x1x2dx\int \frac{x}{\sqrt{1 - x^2}} \, dx

StarStarStarStar

1x2+C\sqrt{1 - x^2} + C

StarStarStarStar

cosh(x)dx\int \cosh(x) \, dx

StarStarStarStar

sinh(x)+C\sinh(x) + C

StarStarStarStar

asec(x)dx\int \text{asec}(x) \, dx

StarStarStarStar

xasec(x)lnx+x21+Cx \text{asec}(x) - \ln|x + \sqrt{x^2 - 1}| + C

StarStarStarStar

exdx\int e^{-x} \, dx

StarStarStarStar

ex+C-e^{-x} + C

StarStarStarStar

cot(x)dx\int \cot(x) \, dx

StarStarStarStar

lnsin(x)+C\ln|\sin(x)| + C

StarStarStarStar

1sin2(x)dx\int \frac{1}{\sin^2(x)} \, dx

StarStarStarStar

cot(x)+C-\cot(x) + C

StarStarStarStar

sec(x)dx\int \sec(x) \, dx

StarStarStarStar

lnsec(x)+tan(x)+C\ln|\sec(x) + \tan(x)| + C

StarStarStarStar

sec(x)tan(x)dx\int \sec(x)\tan(x) \, dx

StarStarStarStar

sec(x)+C\sec(x) + C

StarStarStarStar

tan2(x)dx\int \tan^2(x) \, dx

StarStarStarStar

tan(x)x+C\tan(x) - x + C

StarStarStarStar

csc2(x)dx\int \csc^2(x) \, dx

StarStarStarStar

cot(x)+C-\cot(x) + C

StarStarStarStar

dx1x2\int \frac{dx}{\sqrt{1 - x^2}}

StarStarStarStar

arcsin(x)+C\arcsin(x) + C

StarStarStarStar

sinh2(x)dx\int \sinh^2(x) \, dx

StarStarStarStar

14(sinh(2x)2x)+C\frac{1}{4}(\sinh(2x) - 2x) + C

StarStarStarStar

x2dx\int x^2 \, dx

StarStarStarStar

13x3+C\frac{1}{3}x^3 + C

StarStarStarStar

sinh(x)dx\int \sinh(x) \, dx

StarStarStarStar

cosh(x)+C\cosh(x) + C

StarStarStarStar

xdx\int x \, dx

StarStarStarStar

12x2+C\frac{1}{2}x^2 + C

StarStarStarStar

cos(x)dx\int \cos(x) \, dx

StarStarStarStar

sin(x)+C\sin(x) + C

StarStarStarStar

dx1+x2\int \frac{dx}{1 + x^2}

StarStarStarStar

arctan(x)+C\arctan(x) + C

StarStarStarStar

ln(x)dx\int \ln(x) \, dx

StarStarStarStar

xln(x)x+Cx\ln(x) - x + C

StarStarStarStar

1x2+1dx\int \frac{1}{x^2 + 1} \, dx

StarStarStarStar

arctan(x)+C\text{arctan}(x) + C

StarStarStarStar

xdx\int \sqrt{x} \, dx

StarStarStarStar

23x32+C\frac{2}{3}x^{\frac{3}{2}} + C

StarStarStarStar

e2xdx\int e^{2x} \, dx

StarStarStarStar

12e2x+C\frac{1}{2}e^{2x} + C

StarStarStarStar

tan(x)dx\int \tan(x) \, dx

StarStarStarStar

lncos(x)+C-\ln|\cos(x)| + C

StarStarStarStar

xsin(x)dx\int x \sin(x) \, dx

StarStarStarStar

xcos(x)+sin(x)+C-x \cos(x) + \sin(x) + C

StarStarStarStar

sin(x)dx\int \sin(x) \, dx

StarStarStarStar

cos(x)+C-\cos(x) + C

StarStarStarStar

dxx21\int \frac{dx}{\sqrt{x^2 - 1}}

StarStarStarStar

arcosh(x)+C\text{arcosh}(x) + C

StarStarStarStar

arcsin(x)dx\int \arcsin(x) \, dx

StarStarStarStar

xarcsin(x)+1x2+Cx \arcsin(x) + \sqrt{1 - x^2} + C

StarStarStarStar

x1/3dx\int x^{1/3} \, dx

StarStarStarStar

34x43+C\frac{3}{4}x^{\frac{4}{3}} + C

StarStarStarStar

1xdx\int \frac{1}{x} \, dx

StarStarStarStar

ln(x)+C\ln(|x|) + C

StarStarStarStar

sec2(x)dx\int \sec^2(x) \, dx

StarStarStarStar

tan(x)+C\tan(x) + C

StarStarStarStar

cot2(x)dx\int \cot^2(x) \, dx

StarStarStarStar

cot(x)x+C-\cot(x) - x + C

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