7.3 Integration by Substitution

Method of substitution for integrating composite functions, with worked example.

If the integrand contains a composite function, substitute the inner function.

Evaluate $\displaystyle\int 2x \cos(x^2)\,dx$ .

Let $t = x^2$ , so $dt = 2x\,dx$ .

\int 2x \cos(x^2)\,dx = \int \cos t\,dt = \sin t + C = \sin(x^2) + C

7.2 Standard Integrals

Table of standard integral formulas for common functions.

7.4 Integration by Partial Fractions

Partial fraction decomposition table and worked example.