Question

find the indefinite integral of sec^2(x)tan^3(x)dx

Answer 1

let u =tanx
du=sec^2xdx

Answer 2

so the integral becomes\[\int\limits{u^3du}=\frac{u^4}{4}+C\]

Answer 3

substitute the u=tanx back\[\int\limits{\sec^2xtan^3xdx}=\frac{\tan^4x}{4}+C\]

Answer 4

thank you!