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?

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kallazans	Ssec^3(w)dw is very easy but you need to pay atention! Tweet 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 Recognitions: Gold Member Science Advisor Staff Emeritus	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?