1. integration by parts.

can someone confirm if i am doing this correctly

5xcos(4x) solve using integration by parts

let V=5x so dv/dx=5

du/dx=cos(4x) u=1/4sin4x

5x(1/4sin4x)-int 5(1/4sin4x)

(5x/4)sin4x + (5/16)cos4x

if i am going wrong somewhere can you please explain thanks.

2. Re: integration by parts.

It looks to me that you have correctly applied the method, although don't forget the constant of integration.

If you have doubts about your indefinite integration result, recall that you may use differentiation as a check:

$\frac{d}{dx}\left(\frac{5x}{4}\sin(4x)+\frac{5}{16 }\cos(4x)+C\right)=\frac{5x}{4}(4\cos(4x))+\frac{5 }{4}\sin(4x)-\frac{5}{4}\sin(4x)+0=5x\cos(4x)$

Since the derivative of the anti-derivative is the original integrand, you know the result is correct.