Integral of $\sec^3(x)$

Question

I want to find the integral of $\sec^3(x)$, but I don't know what to do. I tried a double integration by parts to try and solve it in terms of itself, but I ended up getting 0=0. Could I just have a hint, please?

Answer 1

Hint: $$\int\sec^3(x)dx =\int \sec(x)(\tan^2(x)+1)dx =\int \tan^2(x)\sec(x)dx+\int\sec(x)dx$$