I suck at this... just need someone to check. It looks stupid, I am trying some problems online, and didn't even't learn this in school.

Question

solomonzelman · Answer

§ cos^2 x sin(x)  dx = 
(u=cos(x)   )
§ u^2sin(x)  ( 1/-sin(x ) du  =
§ -u^2 du  =          taking the constant out,v
-§ u^2 du  =            applying the power rule
-§ (-u^2+1) / (2+1) = 
sub in cos(x) for u ...

=  -cos{2+1}x  /  2+1  = -cos^3x/3

My final answer is   (-cos^3x/3)+C

solomonzelman · Answer

§ is supposed to be the (indefinite)  integral

solomonzelman · Answer

reposting a little. I forgot a caret -:(

sub in cos(x) for u ...

=  -cos^{2+1}x  /  2+1  = -cos^3x/3

My final answer is   (-cos^3x/3)+C

luigi0210 · Answer

I think it might be easier to change that $cos^2 x$ into $ 1-sin^2 x$

luigi0210 · Answer

Actually, no, sorry, you did it right :P

luigi0210 · Answer

$$\Large \int cos^2 x ~sinx~ dx$$ 
$u=cosx$ $du=-sinxdx$ 
$$\Large -\int u^2du$$ 

$$\Large -\frac{u^3}{3} +C$$ 
Sub back in~

$$\Large -\frac{cos^3~x}{3}+C$$

solomonzelman · Answer

Thank you for your clarification, Luigi !