Solving Integral Problems: uv- \intvdu Method

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The discussion focuses on solving the integral of x sec^2(x) dx using the integration by parts method, specifically the uv - ∫v du approach. The user correctly identifies u as x, du as dx, dv as sec^2(x) dx, and v as tan(x), leading to the expression xtan(x) - ∫tan(x) dx. The final result is confirmed as xtan(x) - ln|cos(x)| + C, with a suggestion that ln|cos(x)| can also be expressed as -ln|sec(x)|. To verify the solution, differentiating the result is recommended to ensure it matches the original integrand.
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\int xsec^2xdx

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

uv- \intvdu
xtanx-\inttanxdx
xtanx-lnlcosxl+C

just wanted to make sure everything looked alright because I am not feeling totally confident about my last step.
 
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... and i just realized i put this in the wrong forum category. my apologies.
 
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.
 

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