# How to Integrate Even Powers of Secants with Tangents

You can integrate even powers of secants with tangents. If you wanted to integrate tan^{m}*x* sec^{n}*x* when *n* is even — for example, tan^{8} *x* sec^{6} *x* — you would follow these steps:

Peel off a sec

^{2}*x*and place it next to the*dx**:*Use the trig identity 1 + tan

^{2 }*x*= sec^{2}*x*to express the remaining secant factors in terms of tangents:Use the variable substitution

*u*= tan*x*and*du*= sec^{2}*x**dx**:*

At this point, the integral is a polynomial, and you can evaluate it.