Integrals of odd powers of sec(x) are never straight forward, unlike their even powered counterparts. They get exponentially more difficult as the odd power increases. The integral of sec3(x) is a classic integral that is still manageable by conventional analytical methods.
Probably the most straight forward approach is to use integration by parts. To do this, we can write the integral as:
∫sec3(x)dx = ∫sec(x)sec2(x)dx
So now we have the 2 parts required for I.B.P. if we let
u = sec(x) and dv = sec2(x)dx
Please watch the video to see how this integral is solved.
Suggested videos:
Integration of sec(x): https://youtu.be/9pG-1NG2Kqs
Derivative of sec(x): https://youtu.be/_BGccPnemDA
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