Integration help

For integration by substitution I get stuck on which part to make u

For e.g for this q I made cosx equal to u but the ms has Sinx so I got the whole q wrong how would I know what to make u

For integration by substitution I get stuck on which part to make u

For e.g for this q I made cosx equal to u but the ms has Sinx so I got the whole q wrong how would I know what to make u

if u rewrite this a 3 f cosx(sinx) ^2 .dx then you can see the (sinx) in the brackets would be easiest to put as u because du/dx is -cosx so du would be cosx so you would have f (sinx)^2 cosx.dx become f u^2 .du then integrating u^2 would be 1/3 u^3 +c and then youd sub sinx back in so 1/3 sin^3x + c. lemme know if thats right

This is not quite right. Easiest way to do this is with the Reverse Chain Rule. Raise sin^2(x) to sin^3(x) and find the derivative. Probably best to use chain rule here, and you will get 3cosxsin^2x, which is precisely our original integral.

Hence, it is sin^3(x) + c.

Edit: Exactly what old_engineer said above! I didn't see your reply.