Integral [(cosx)^3-(sinx)^2]dx/(cosx)2
Can i cancel the cosx leaving cosx in numerator before I integrate?
If anyone could help with integrating this problem -
You have the right idea.
Split up the integrand:
$\displaystyle \frac{\cos^3x-\sin^2x}{\cos^2x}=\frac{\cos^3x}{\cos^2x}-\frac{\sin^2x}{\cos^2x}=\cos x-\tan^2x$
Now can you integrate $\displaystyle \int \cos x-\tan^2x\,dx$?
hint: $\displaystyle \tan^2x=\sec^2x-1$
I hope this clarifies things!
--Chris