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.
| Question | Answer |
|---|---|
| $$ \int \! e^x \,\,\, \mathrm{d} x $$ | $$ e^x + C $$ |
| $$ \int \! \cos x \,\,\, \mathrm{d} x $$ | $$ \sin x + C $$ |
| $$ \int \! \sin x \,\,\, \mathrm{d} x $$ | $$ -\cos x + C $$ |
| $$ \int \! A \,\,\, \mathrm{d} x $$ | $$ Ax + C $$ |
| $$ \int \! x^n \,\,\, \mathrm{d} x $$ | $$ \frac{1}{n+1} x^{n+1} + C,\, n \neq -1 $$ |
| $$ \int \! \ln(x) \,\, \mathrm{d} x $$ | $$ x\ln(x) - x + C $$ |
| $$ \int \! \frac{1}{x} \,\, \mathrm{d} x $$ | $$ \ln |x| + C $$ |
| $$ \int \! a^x \, \mathrm{d} x $$ | $$ \frac{a^x}{\ln a} + C $$ |
| $$ \int \! xe^x \, \mathrm{d} x $$ | $$ (x-1) e^x + C $$ |
| 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 \( du = g'(x)dx \) |
| $$ \int \! \frac{1}{ax + b} \, \mathrm{d}x $$ | $$ \frac{1}{a} \ln|ax+b| + C $$ |
| $$ \int \! \frac{\mathrm{d}x}{\sqrt{1-x^2}} $$ | $$ \arcsin x + C $$ |
| $$ \int \! \tan x \, \mathrm{d}x $$ | $$ - \ln|\cos x| + C $$ |
| $$ \int \! \frac{\mathrm{d}x}{1+x^2} $$ | $$ \arctan x + C $$ |
