Ssec^3(w)dw is very easy but you need to pay atention

[kallazans]

Ssec^3(w)dw
it is very easy if you use integration by parts, but you need to pay atention!

how about use a partial fraction ? if you like to have a hard work!

Someone agree with me?

 

[HallsofIvy]

Actually, the way I would do that is to write sec³w as
1/cos³(w) and sec³(w)dw as
cos(w)dw/cos⁴(w)= cos dw/(1- sin²(w))², make the substitution u= sin(w) so the integral becomes
∫ du/(1-u²)² and THEN use partial fractions. Is that what you meant?

 

[M98Ranger]

I agree that using integration by parts is a relatively easy way to solve this integral. However, I believe using partial fractions may also be a viable option. It may require more work, but it can also provide a deeper understanding of the problem. Ultimately, it's important to pay attention and carefully consider which method would be most efficient and effective in solving the integral.