Maths  Integration by Parts
posted by Anonymous on .
Question 1
ç e^2x Cos(4x) dx
Question 2)
ç ãx sin(x) dx
Question 3)
ç x^2 sin(x) dx

I'll do #1, you can show us where you get stuck on the others.
Let I = ∫e^2x cos4x dx
u=cos 4x
du = 4sin4x dx
dv = e^2x dx
v = 1/2 e^2x
I = uv  ∫v du
= 1/2 e^2x cos4x  ∫2e^2x sin4x dx
Now do it again, letting u = sin4x
I = 1/2 e^2x cos4x + (e^2x sin4x  ∫4e^2x cos4x dx)
= 1/2 e^2x cos4x + e^2x sin4x  4I
5I = 1/2 e^2x cos4x + e^2x sin4x
I = 1/10 e^2x (cos4x + 2sin4x)