Solving Integral Problems: uv- \intvdu Method

[brutalmadness]

$$\int$$ xsec^2xdx

u=x du=dx dv=sec^2xdx v=tanx

uv- $$\int$$vdu
xtanx-$$\int$$tanxdx
xtanx-lnlcosxl+C

just wanted to make sure everything looked alright because I am not feeling totally confident about my last step.

 

[brutalmadness]

... and i just realized i put this in the wrong forum category. my apologies.

 

[rock.freak667]

Yes it is correct but if you wanted to you could write -ln|cosx| as ln|secx| but it is still correct. You could always check it back by differentiating it and see if you get back the integrand.