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Explore tens of thousands of sets crafted by our community.
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Calculus Integrals
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Flashcards
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∫dxx2+1\int \frac{dx}{\sqrt{x^2 + 1}}∫x2+1dx
arsinh(x)+C\text{arsinh}(x) + Carsinh(x)+C
∫csc(x) dx\int \csc(x) \, dx∫csc(x)dx
−ln∣csc(x)+cot(x)∣+C-\ln|\csc(x) + \cot(x)| + C−ln∣csc(x)+cot(x)∣+C
∫1cos2(x) dx\int \frac{1}{\cos^2(x)} \, dx∫cos2(x)1dx
tan(x)+C\tan(x) + Ctan(x)+C
∫arctan(x) dx\int \arctan(x) \, dx∫arctan(x)dx
xarctan(x)−12ln(1+x2)+Cx \arctan(x) - \frac{1}{2} \ln(1+x^2) + Cxarctan(x)−21ln(1+x2)+C
∫xcos(x) dx\int x \cos(x) \, dx∫xcos(x)dx
xsin(x)+cos(x)+Cx \sin(x) + \cos(x) + Cxsin(x)+cos(x)+C
∫ex dx\int e^x \, dx∫exdx
ex+Ce^x + Cex+C
∫11−x dx\int \frac{1}{1 - x} \, dx∫1−x1dx
−ln(∣1−x∣)+C-\ln(|1 - x|) + C−ln(∣1−x∣)+C
∫ln(x)2 dx\int \ln(x)^2 \, dx∫ln(x)2dx
xln(x)2−2xln(x)+2x+Cx\ln(x)^2 - 2x\ln(x) + 2x + Cxln(x)2−2xln(x)+2x+C
∫cosh2(x) dx\int \cosh^2(x) \, dx∫cosh2(x)dx
14(sinh(2x)+2x)+C\frac{1}{4}(\sinh(2x) + 2x) + C41(sinh(2x)+2x)+C
∫x3 dx\int x^3 \, dx∫x3dx
14x4+C\frac{1}{4}x^4 + C41x4+C
∫x1−x2 dx\int \frac{x}{\sqrt{1 - x^2}} \, dx∫1−x2xdx
1−x2+C\sqrt{1 - x^2} + C1−x2+C
∫cosh(x) dx\int \cosh(x) \, dx∫cosh(x)dx
sinh(x)+C\sinh(x) + Csinh(x)+C
∫asec(x) dx\int \text{asec}(x) \, dx∫asec(x)dx
xasec(x)−ln∣x+x2−1∣+Cx \text{asec}(x) - \ln|x + \sqrt{x^2 - 1}| + Cxasec(x)−ln∣x+x2−1∣+C
∫e−x dx\int e^{-x} \, dx∫e−xdx
−e−x+C-e^{-x} + C−e−x+C
∫cot(x) dx\int \cot(x) \, dx∫cot(x)dx
ln∣sin(x)∣+C\ln|\sin(x)| + Cln∣sin(x)∣+C
∫1sin2(x) dx\int \frac{1}{\sin^2(x)} \, dx∫sin2(x)1dx
−cot(x)+C-\cot(x) + C−cot(x)+C
∫sec(x) dx\int \sec(x) \, dx∫sec(x)dx
ln∣sec(x)+tan(x)∣+C\ln|\sec(x) + \tan(x)| + Cln∣sec(x)+tan(x)∣+C
∫sec(x)tan(x) dx\int \sec(x)\tan(x) \, dx∫sec(x)tan(x)dx
sec(x)+C\sec(x) + Csec(x)+C
∫tan2(x) dx\int \tan^2(x) \, dx∫tan2(x)dx
tan(x)−x+C\tan(x) - x + Ctan(x)−x+C
∫csc2(x) dx\int \csc^2(x) \, dx∫csc2(x)dx
∫dx1−x2\int \frac{dx}{\sqrt{1 - x^2}}∫1−x2dx
arcsin(x)+C\arcsin(x) + Carcsin(x)+C
∫sinh2(x) dx\int \sinh^2(x) \, dx∫sinh2(x)dx
14(sinh(2x)−2x)+C\frac{1}{4}(\sinh(2x) - 2x) + C41(sinh(2x)−2x)+C
∫x2 dx\int x^2 \, dx∫x2dx
13x3+C\frac{1}{3}x^3 + C31x3+C
∫sinh(x) dx\int \sinh(x) \, dx∫sinh(x)dx
cosh(x)+C\cosh(x) + Ccosh(x)+C
∫x dx\int x \, dx∫xdx
12x2+C\frac{1}{2}x^2 + C21x2+C
∫cos(x) dx\int \cos(x) \, dx∫cos(x)dx
sin(x)+C\sin(x) + Csin(x)+C
∫dx1+x2\int \frac{dx}{1 + x^2}∫1+x2dx
arctan(x)+C\arctan(x) + Carctan(x)+C
∫ln(x) dx\int \ln(x) \, dx∫ln(x)dx
xln(x)−x+Cx\ln(x) - x + Cxln(x)−x+C
∫1x2+1 dx\int \frac{1}{x^2 + 1} \, dx∫x2+11dx
arctan(x)+C\text{arctan}(x) + Carctan(x)+C
∫x dx\int \sqrt{x} \, dx∫xdx
23x32+C\frac{2}{3}x^{\frac{3}{2}} + C32x23+C
∫e2x dx\int e^{2x} \, dx∫e2xdx
12e2x+C\frac{1}{2}e^{2x} + C21e2x+C
∫tan(x) dx\int \tan(x) \, dx∫tan(x)dx
−ln∣cos(x)∣+C-\ln|\cos(x)| + C−ln∣cos(x)∣+C
∫xsin(x) dx\int x \sin(x) \, dx∫xsin(x)dx
−xcos(x)+sin(x)+C-x \cos(x) + \sin(x) + C−xcos(x)+sin(x)+C
∫sin(x) dx\int \sin(x) \, dx∫sin(x)dx
−cos(x)+C-\cos(x) + C−cos(x)+C
∫dxx2−1\int \frac{dx}{\sqrt{x^2 - 1}}∫x2−1dx
arcosh(x)+C\text{arcosh}(x) + Carcosh(x)+C
∫arcsin(x) dx\int \arcsin(x) \, dx∫arcsin(x)dx
xarcsin(x)+1−x2+Cx \arcsin(x) + \sqrt{1 - x^2} + Cxarcsin(x)+1−x2+C
∫x1/3 dx\int x^{1/3} \, dx∫x1/3dx
34x43+C\frac{3}{4}x^{\frac{4}{3}} + C43x34+C
∫1x dx\int \frac{1}{x} \, dx∫x1dx
ln(∣x∣)+C\ln(|x|) + Cln(∣x∣)+C
∫sec2(x) dx\int \sec^2(x) \, dx∫sec2(x)dx
∫cot2(x) dx\int \cot^2(x) \, dx∫cot2(x)dx
−cot(x)−x+C-\cot(x) - x + C−cot(x)−x+C
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