How to integrate sec^2(x)tan^3(x)?

To integrate sec^2(x)tan^3(x), use substitution with u = tan(x) and du = sec^2(x)dx.

To integrate sec^2(x)tan^3(x), we can use substitution with u = tan(x) and du = sec^2(x)dx. This gives us:

∫sec^2(x)tan^3(x)dx = ∫u^3du

Integrating u^3 gives us:

∫u^3du = (1/4)u^4 + C

Substituting back in for u, we get:

(1/4)tan^4(x) + C

Therefore, the final answer is (1/4)tan^4(x) + C.