I need help with solving the integral of:

I got:

as the answer but I don't think it's correct...

I tried to use the table of integrals I have but I couldn't find something that met that scenario so I ended up substitutingufor sin(x) as well asdufor cos(x) and had the following before substituting u back in, I used the trig. property of cos^2(x) = 1-sin^2(x):

Integral of

Then:

Integral of

Thanks,