Here’s how you integrate a trig integral that contains tangents and secants where the secant power is even and positive. Like with all tangent/secant integrals, you use the tangent-secant version of the Pythagorean identity,
![image0.png](https://cdn.prod.website-files.com/6634a8f8dd9b2a63c9e6be83/669e25cf3924380dc89b38df_204783.image0.png)
Lop off a secant-squared(x) factor and move it to the right.
Convert the remaining secants to tangents with the Pythagorean identity,
Solve by substitution, where u = tan(x) and