Chapter 8 - Integration Techniques, L'Hopital's Rule, and Improper Integrals - 8.3 Exercises - Page 530: 28

$\tan^2\left(\frac{x}{2}\right) +C$

Find the indefinite integral $\int sec^2\frac{x}{2}tan\frac{x}{2}dx$ Use u-substitution, let $u=tan\frac{x}{2}$, $du=\frac{1}{2}sec^2\frac{x}{2}dx$ $2\int udu$ $u^2 +C$ $\tan^2\left(\frac{x}{2}\right) +C$