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## Calculus 2

### Unit 1: Lesson 11

Indefinite integrals of common functions

# Common integrals review

Review the integration rules for all the common function types.

## Polynomials

integral, x, start superscript, n, end superscript, d, x, equals, start fraction, x, start superscript, n, plus, 1, end superscript, divided by, n, plus, 1, end fraction, plus, C

\begin{aligned} \displaystyle\int\sqrt[\Large m]{x^n}\,dx&=\displaystyle\int x^{^{\Large\frac{n}{m}}}\,dx \\\\ &=\dfrac{x^{^{\Large \frac{n}{m}+1}}}{\dfrac{n}{m}+1}+C \end{aligned}
Want to practice integrating polynomials and radicals? Check out these exercises:

## Trigonometric functions

integral, sine, left parenthesis, x, right parenthesis, d, x, equals, minus, cosine, left parenthesis, x, right parenthesis, plus, C
integral, cosine, left parenthesis, x, right parenthesis, d, x, equals, sine, left parenthesis, x, right parenthesis, plus, C
integral, \sec, squared, left parenthesis, x, right parenthesis, d, x, equals, tangent, left parenthesis, x, right parenthesis, plus, C
integral, \csc, squared, left parenthesis, x, right parenthesis, d, x, equals, minus, cotangent, left parenthesis, x, right parenthesis, plus, C
integral, \sec, left parenthesis, x, right parenthesis, tangent, left parenthesis, x, right parenthesis, d, x, equals, \sec, left parenthesis, x, right parenthesis, plus, C
integral, \csc, left parenthesis, x, right parenthesis, cotangent, left parenthesis, x, right parenthesis, d, x, equals, minus, \csc, left parenthesis, x, right parenthesis, plus, C
Want to practice integrating trigonometric functions? Check out these exercises:

## Exponential functions

integral, e, start superscript, x, end superscript, d, x, equals, e, start superscript, x, end superscript, plus, C
integral, a, start superscript, x, end superscript, d, x, equals, start fraction, a, start superscript, x, end superscript, divided by, natural log, left parenthesis, a, right parenthesis, end fraction, plus, C

## Integrals that are logarithmic functions

integral, start fraction, 1, divided by, x, end fraction, d, x, equals, natural log, vertical bar, x, vertical bar, plus, C
Want to learn more about integrating exponential functions and start fraction, 1, divided by, x, end fraction? Check out this video.
Want to practice integrating exponential functions and start fraction, 1, divided by, x, end fraction? Check out this exercise.

## Integrals that are inverse trigonometric functions

integral, start fraction, 1, divided by, square root of, a, squared, minus, x, squared, end square root, end fraction, d, x, equals, \arcsin, left parenthesis, start fraction, x, divided by, a, end fraction, right parenthesis, plus, C
integral, start fraction, 1, divided by, a, squared, plus, x, squared, end fraction, d, x, equals, start fraction, 1, divided by, a, end fraction, \arctan, left parenthesis, start fraction, x, divided by, a, end fraction, right parenthesis, plus, C