Chapter 8 - Integration Techniques, L'Hopital's Rule, and Improper Integrals - 8.1 Exercises - Page 512: 41

$\frac 1 2 ln|cos(\frac 2 t)|+C$

$Let u=cos(\frac 2 t), du=\frac {2sin(\frac 2 t)}{t^2}dt$ $\int \frac{tan\frac2 t}{t^2}dt$ $\frac1 2 \int \frac 1{cos(\frac 2 t)}[\frac {2sin(\frac 2 t)}{t^2}]dt$ $\frac 1 2 ln|cos(\frac 2 t)|+C$