Integrating a Trigonometric Function with a Power of Secant: tan(x)sec^4(x)

[mk200789]

Homework Statement

integrate tan(x)sec^4(x) dx

Homework Equations

The Attempt at a Solution

int tan(x)sec^4(x) dx
= int tan(x)sec^2(x)sec^2(x) dx
= int tan(x)sec^2(x) (tan^2(x)+1) dx

let u = tanx ==> du = sec^2(x) dx

= int usec^2(x) (u^2 + 1) /sec^2(x) du
= int u(u^2+1) du
= u^4/4 + u^2/2 + C
and then replace the u with tanx

am i doing this correct?

 

[Char. Limit]

Absolutely. If you want, you can unfactor the answer, but it isn't necessary.

 

[mk200789]

ttthank you!