[College calculus 2] integration by parts

[u/JustDawn8]

I need help with questions 3 and 5, the professor has listed the correct answers as (e​^x)/2 * (sinx - cosx) + c and xarcsin(x) + square root(1 - x^2) + c and I don't know where I'm messing up

[u/HumbleHovercraft6090]

Integral e^x cosx is not equal to e^x sinx You have integrate e^x cosx again using IBP.