Common integrals review

Review the integration rules for all the common function types.

Polynomials

\int x^{n} d x = \frac{x^{n + 1}}{n + 1} + C

\begin{aligned} \int \sqrt[m]{x^{n}} d x & = \int x^{^{\frac{n}{m}}} d x \\ = \frac{x^{^{\frac{n}{m} + 1}}}{\frac{n}{m} + 1} + C \end{aligned}

Want to learn more about integrating polynomials and radicals? Check out this video.

Want to practice integrating polynomials and radicals? Check out these exercises:

\int \sin (x) d x = - \cos (x) + C

\int \cos (x) d x = \sin (x) + C

\int \sec^{2} (x) d x = \tan (x) + C

\int \csc^{2} (x) d x = - \cot (x) + C

\int \sec (x) \tan (x) d x = \sec (x) + C

\int \csc (x) \cot (x) d x = - \csc (x) + C

Want to learn more about integrating trigonometric functions? Check out this video.

Want to practice integrating trigonometric functions? Check out these exercises:

\int e^{x} d x = e^{x} + C

\int a^{x} d x = \frac{a^{x}}{\ln (a)} + C

\int \frac{1}{x} d x = \ln | x | + C

Want to learn more about integrating exponential functions and $\frac{1}{x}$ ‍? Check out this video.

Want to practice integrating exponential functions and $\frac{1}{x}$ ‍? Check out this exercise.

\int \frac{1}{\sqrt{a^{2} - x^{2}}} d x = \arcsin (\frac{x}{a}) + C

\int \frac{1}{a^{2} + x^{2}} d x = \frac{1}{a} \arctan (\frac{x}{a}) + C

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