Thread: integration questions stuck :(

Hey guy i gt this questions on integration which i am not sure how to approach. I have uploaded the question via jpg file.

For the first questions i attempted to intergrate by parts and let u=e^tanx
du= tane^tanx.dx, dv/dx = cos^2x and v = (sin^3x)/3, am i correct so far?

As a results i was left with:

e^tanx . (sin^3x/3) - Int (sin^3X/3) . tane^tanx

what do i do now if in fact i am on the correct path i would assume to integrate it again but that seems too difficult and deafeats the purpose of the IBP. Was i supposed to use IBP? Any help would be greatly appreciated.

Originally Posted by Latkan

Hey guy i gt this questions on integration which i am not sure how to approach. I have uploaded the question via jpg file.

For the first questions i attempted to intergrate by parts and let u=e^tanx
du= tane^tanx.dx, dv/dx = cos^2x and v = (sin^3x)/3, am i correct so far?

As a results i was left with:

e^tanx . (sin^3x/3) - Int (sin^3X/3) . tane^tanx

what do i do now if in fact i am on the correct path i would assume to integrate it again but that seems too difficult and deafeats the purpose of the IBP. Was i supposed to use IBP? Any help would be greatly appreciated.

This looks like a simple substituion



Because

Let . Hence


Now to work out our limits in terms of u. For this simply sub the limit into our expression for u.






Now we can put all these expressions into the integral to give:



Which is a very simple integral and can be solved directly because we changed the limits