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Calculus Integrals

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StarStarStarStar

∫x dx\int x \, dx

StarStarStarStar

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

StarStarStarStar

∫x2 dx\int x^2 \, dx

StarStarStarStar

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

StarStarStarStar

∫dx1−x2\int \frac{dx}{\sqrt{1 - x^2}}

StarStarStarStar

arcsin⁡(x)+C\arcsin(x) + C

StarStarStarStar

∫dx1+x2\int \frac{dx}{1 + x^2}

StarStarStarStar

arctan⁡(x)+C\arctan(x) + C

StarStarStarStar

∫dxx2+1\int \frac{dx}{\sqrt{x^2 + 1}}

StarStarStarStar

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

StarStarStarStar

∫dxx2−1\int \frac{dx}{\sqrt{x^2 - 1}}

StarStarStarStar

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

StarStarStarStar

∫e−x dx\int e^{-x} \, dx

StarStarStarStar

−e−x+C-e^{-x} + C

StarStarStarStar

∫ln⁡(x) dx\int \ln(x) \, dx

StarStarStarStar

xln⁡(x)−x+Cx\ln(x) - x + C

StarStarStarStar

∫11−x dx\int \frac{1}{1 - x} \, dx

StarStarStarStar

−ln⁡(∣1−x∣)+C-\ln(|1 - x|) + C

StarStarStarStar

∫x1−x2 dx\int \frac{x}{\sqrt{1 - x^2}} \, dx

StarStarStarStar

1−x2+C\sqrt{1 - x^2} + C

StarStarStarStar

∫e2x dx\int e^{2x} \, dx

StarStarStarStar

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

StarStarStarStar

∫arcsin⁡(x) dx\int \arcsin(x) \, dx

StarStarStarStar

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

StarStarStarStar

∫x3 dx\int x^3 \, dx

StarStarStarStar

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

StarStarStarStar

∫1x2+1 dx\int \frac{1}{x^2 + 1} \, dx

StarStarStarStar

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

∫sinh⁡(x) dx\int \sinh(x) \, dx

StarStarStarStar

cosh⁡(x)+C\cosh(x) + C

StarStarStarStar

∫cosh⁡(x) dx\int \cosh(x) \, dx

StarStarStarStar

sinh⁡(x)+C\sinh(x) + C

StarStarStarStar

∫tan⁡(x) dx\int \tan(x) \, dx

StarStarStarStar

−ln⁡∣cos⁡(x)∣+C-\ln|\cos(x)| + C

StarStarStarStar

∫cot⁡(x) dx\int \cot(x) \, dx

StarStarStarStar

ln⁡∣sin⁡(x)∣+C\ln|\sin(x)| + C

StarStarStarStar

∫x dx\int \sqrt{x} \, dx

StarStarStarStar

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

StarStarStarStar

∫x1/3 dx\int x^{1/3} \, dx

StarStarStarStar

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

StarStarStarStar

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

StarStarStarStar

tan⁡(x)+C\tan(x) + C

StarStarStarStar

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

StarStarStarStar

−cot⁡(x)+C-\cot(x) + C

StarStarStarStar

∫cos⁡(x) dx\int \cos(x) \, dx

StarStarStarStar

sin⁡(x)+C\sin(x) + C

StarStarStarStar

∫ln⁡(x)2 dx\int \ln(x)^2 \, dx

StarStarStarStar

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

StarStarStarStar

∫xsin⁡(x) dx\int x \sin(x) \, dx

StarStarStarStar

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

StarStarStarStar

∫xcos⁡(x) dx\int x \cos(x) \, dx

StarStarStarStar

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

StarStarStarStar

∫sec⁡(x) dx\int \sec(x) \, dx

StarStarStarStar

ln⁡∣sec⁡(x)+tan⁡(x)∣+C\ln|\sec(x) + \tan(x)| + C

StarStarStarStar

∫csc⁡(x) dx\int \csc(x) \, dx

StarStarStarStar

−ln⁡∣csc⁡(x)+cot⁡(x)∣+C-\ln|\csc(x) + \cot(x)| + C

StarStarStarStar

∫tan⁡2(x) dx\int \tan^2(x) \, dx

StarStarStarStar

tan⁡(x)−x+C\tan(x) - x + C

StarStarStarStar

∫cot⁡2(x) dx\int \cot^2(x) \, dx

StarStarStarStar

−cot⁡(x)−x+C-\cot(x) - x + C

StarStarStarStar

∫sinh⁡2(x) dx\int \sinh^2(x) \, dx

StarStarStarStar

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

StarStarStarStar

∫cosh⁡2(x) dx\int \cosh^2(x) \, dx

StarStarStarStar

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

StarStarStarStar

∫asec(x) dx\int \text{asec}(x) \, dx

StarStarStarStar

xasec(x)−ln⁡∣x+x2−1∣+Cx \text{asec}(x) - \ln|x + \sqrt{x^2 - 1}| + C

StarStarStarStar

∫sin⁡(x) dx\int \sin(x) \, dx

StarStarStarStar

−cos⁡(x)+C-\cos(x) + C

StarStarStarStar

∫ex dx\int e^x \, dx

StarStarStarStar

ex+Ce^x + C

StarStarStarStar

∫1x dx\int \frac{1}{x} \, dx

StarStarStarStar

ln⁡(∣x∣)+C\ln(|x|) + C

StarStarStarStar

∫sec⁡2(x) dx\int \sec^2(x) \, dx

StarStarStarStar

tan⁡(x)+C\tan(x) + C

StarStarStarStar

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

StarStarStarStar

sec⁡(x)+C\sec(x) + C

StarStarStarStar

∫csc⁡2(x) dx\int \csc^2(x) \, dx

StarStarStarStar

−cot⁡(x)+C-\cot(x) + C

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