Hi I can't figure out how to do part b from both questions linked. For question 1 I can't figure out how to use recognition to rearrange the equation (which I'm pretty sure is the method they want you to use) and I only got so far as rearranging for the integral of xcos^n(x) from the original equation. Question 2 they most likely expect you to use recognition too. I tried to change all the x's in part a) ii into (pi/2 - x) and then isolate the xcos(x) integral, but got (pi-x)sin(x)-cos(x) as a final answer which is wrong too (I know using integration by parts would make things 20 times less complicated but I need those working marks if I get the wrong answer). As always help is appreciated.

**Question 1:** From what you said, you did part (a), you should have gotten:

(using the chain rule and product rule).

So

. Rearranging for cos^n(x)

Integrating both sides (and flipping the equation):

*Let ***Notice that the integrand on the RHS of the equation from before is just** So

So substituting the previous result back in:

Adding

to both sides

The left hand side is just

, So divide through by

to get the final value of the integral:

As for the second question you had, you may have to use a similar technique. If you need further help feel free to reply.