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Riemann Integration

Flashcards

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$x$

$\int x\,dx = \frac{1}{2}x^2 + C$

$\cos(x)$

$\int \cos(x)\,dx = \sin(x) + C$

$\frac{1}{\sqrt{x}}$

$\int \frac{1}{\sqrt{x}}\,dx = 2\sqrt{x} + C$

$\ln(x)$

$\int \ln(x)\,dx = x\ln(x) - x + C$

$e^{2x}$

$\int e^{2x}\,dx = \frac{1}{2}e^{2x} + C$

$\sin^2(x)$

$\int \sin^2(x)\,dx = \frac{1}{2}(x - \sin(x)\cos(x)) + C$

$\tan(x)$

$\int \tan(x)\,dx = -\ln|\cos(x)| + C$

$\sec(x)$

$\int \sec(x)\,dx = \ln|\sec(x) + \tan(x)| + C$

$\frac{1}{1 + x^2}$

$\int \frac{1}{1 + x^2}\,dx = \arctan(x) + C$

$\sinh(x)$

$\int \sinh(x)\,dx = \cosh(x) + C$

$\cosh(x)$

$\int \cosh(x)\,dx = \sinh(x) + C$

$\arcsin(x)$

$\int \arcsin(x)\,dx = x\arcsin(x) + \sqrt{1-x^2} + C$

$e^x$

$\int e^x\,dx = e^x + C$

$\frac{1}{x}$

$\int \frac{1}{x}\,dx = \ln|x| + C$

$\sin(x)$

$\int \sin(x)\,dx = -\cos(x) + C$

$1$

$\int 1\,dx = x + C$

$x^2$

$\int x^2\,dx = \frac{1}{3}x^3 + C$

$\sec^2(x)$

$\int \sec^2(x)\,dx = \tan(x) + C$

$\sqrt{x}$

$\int \sqrt{x}\,dx = \frac{2}{3}x^{\frac{3}{2}} + C$

$x^3$

$\int x^3\,dx = \frac{1}{4}x^4 + C$

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