Find the integral of (x cos(2x)) dx, using integration by parts.
I used x as dv/dx and cos(2x) as u.
So v = (v^2/2) and (du/dx) = -2sin(2x)
I am having problems using the formula:
I = uv - Integral ( u' v ) dx. Can anyone help me with this as I can't get the correct answer.
If you have troubles integrating this, you can substitute before starting.
So it becomes which is easier to integrate.
So for this example:
Integral (Limits 0 to 1) (2x-1) e^(3x+2).
I set (dv/dx)=(2x-1) so, v=(((2x-1)^2)/2)
and u=e^(3x+2) so, u'=3e^(3x+2).
Am I correct so far. Then using the formula:
e^(3x+2).(((2x-1)^2)/2) - (Integral of) (3e^(3x+2)).(((2x-1)^2)/2).
Would you use integration by parts again for the second part? I can't seem to do this. Please help.