# Common Integrals and Integrals Properties Flashcards

This set of flashcards contains flashcards on the topic of common integrals and integrals properties. It was created using Memjogger - an online flashcards and repetitive learning tool.

$$\int \! \cos x \,\,\, \mathrm{d} x$$ $$\sin x + C$$
$$\int \! \sin x \,\,\, \mathrm{d} x$$ $$-\cos x + C$$
$$\int \! A \,\,\, \mathrm{d} x$$ $$Ax + C$$
$$\int \! x^n \,\,\, \mathrm{d} x$$ $$\frac{1}{n+1} x^{n+1} + C,\, n \neq -1$$
$$\int \! \frac{1}{x} \,\, \mathrm{d} x$$ $$\ln |x| + C$$
$$\int \! \ln(x) \,\, \mathrm{d} x$$ $$x\ln(x) - x + C$$
$$\int \! a^x \, \mathrm{d} x$$ $$\frac{a^x}{\ln a} + C$$
$$\int \! xe^x \, \mathrm{d} x$$ $$(x-1) e^x + C$$
Integration by parts $$\int \! f(x)g'(x) \, \mathrm{d} x = f(x)g(x) - \int \! f'(x)g(x) \, \mathrm{d}x$$
Integration by substitution $$\int_a^b \! f(g(x))g'(x) \, \mathrm{d} x = f(x)g(x) - \int_{g(a)}^{g(b)} \! f(u) \, \mathrm{d}u$$ where $$u = dx$$ and $$du = g'(x)dx$$
$$\int \! \frac{1}{ax + b} \, \mathrm{d}x$$ $$\frac{1}{a} \ln|ax+b| + C$$
$$\int \! e^x \,\,\, \mathrm{d} x$$ $$e^x + C$$
$$\int \! \frac{\mathrm{d}x}{\sqrt{1-x^2}}$$ $$\arcsin x + C$$
$$\int \! \tan x \, \mathrm{d}x$$ $$- \ln|\cos x| + C$$
$$\int \! \frac{\mathrm{d}x}{1+x^2}$$ $$\arctan x + C$$
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