Problem with integration by parts exercise

[syncmaster913n]

I have this integration problem in my textbook. Below are the steps I took to solve it:



Now, integrating the right-most integral again:



Now combining:





However, the textbook states the solution should be the following (without providing any steps):



I'm assuming I must have messed up a -/+ somewhere, but cannot find where. Could someone tell me what's wrong with my solution?

Thank you.

 

[syncmaster913n]

Nevermind, I see the error now. In step 3 (when combining) I forgot to multiply the second integral by the negative sign. Should be -4 (.....)

 

[lookagain]

View attachment 7680

Don't forget the "+C" at the end.

 

[syncmaster913n]

Yes, thank you.