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## 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?