Question

Integrate. cos^2x tan^3x

Answer 1

hint:
\[\tan^3 x \implies \frac{\sin^3 x}{\cos^3 x}\]

Answer 2

Yeah I think I got it.

Answer 3

congrats :D

Answer 4

I got up to \[\int\limits_{}^{}(1/2-1/2\cos2x)\sin(x) \cos ^{-1} (x)\]

Answer 5

Yeah, now I'm lost.

Answer 6

oh got it's \[\int\limits_{}^{}(1-\cos^2 x)\sin(x) \cos ^{-1} x\] u=cosx

Answer 7

\[\cos^2(x)\frac{\sin^3 x}{\cos^3 x}=\frac{\sin^3(x)}{\cos(x)}=\sin(x)\frac{\sin^2(x)}{\cos(x)}\]

\[=\sin(x)\frac{1-\cos^2(x)}{\cos(x)}\]


...yep

Answer 8

Thanks!