Maths C4 Integration Urgent

http://pmt.physicsandmathstutor.com/download/Maths/A-level/C4/Topic-Qs/Edexcel-Set-1/C4%20Integration%20-%20By%20parts.pdf

Q4C Page 3
MS is on the top of page 12

I did everything correctly up to the point where I had: ∫(u-1)^2/u
What I did was separated this into ∫(u-1)^2*1/u which I then integrated to ln(1+e^x) + 1/2(e^2x) after subbing back the x

I don't understand why my method is incorrect, I understand what the MS has done but not why my method doesn't work. Thanks in advance!

EDIT: I realise my answer doesn't show what the question wants me to show however why is my method incorrect?

@Notnek


Thanks in advance...

How does $\displaystyle \int (u-1)^2 \cdot \dfrac{1}{u}.du$ integrate to $\ln u + \frac{1}{2}(u-1)^2$ ?? Explain your thought process.

I can’t help right now but you didn’t get an answer because you didn’t post in the maths forum. I’ve moved this thread for you now.

How does $\displaystyle \int (u-1)^2 \cdot \dfrac{1}{u}.du$ integrate to $\ln u + \frac{1}{2}(u-1)^2$ ?? Explain your thought process.

Irrelevant to the question in OP, but when integrating y^1/3 why doesn;t it integrate to ln(y^1/3)?

I think you’ll need to explain why you think it would. Have you tried differentiating ln(y^1/3)?

Oh I see now
1/3yln(y)^2/3 =/= y^1/3

Thanks, I always forget to differetiate to check if it actually works.

I don’t know how you managed to get that when differentiating ln(y^1/3).