Hi, I'm having a little trouble solving an integral by parts, here is what I have so far:
The integral of xsin(x/2)dx
I let u(random letter) = x.
so du = dx.
and dv = sin(x/2).
and v = cos(x/2).
Then I do UV-the integral of dvu.
I then get:
xCos(x/2) - the integral of sin(x/2)x dx
And this is the part I get confused on, am I supposed to do:
xCos(x/2) - -Cos(x/2)x dx
which means
xCos(x/2) + Cos(x/2)x dx
And from here I am lost, does anyone know what I should do?
Ok, thanks . I understand why my v was wrong now. I still don't understand why there would be a 2 in front of the second cos though? because I'm multiplying u*v - the integral of sin(1/2 x) x
So how does that come out to be -2cos etc? And plus my book is telling me the answer is something like
-2xCos(x/2)+4Sin(x/2)+c
I'm completely lost on everything except how to get the c haha.