how can i integrate
∫x*(sin(x))^2

Question

how can i integrate
∫x*(sin(x))^2

anonymous · Answer

Intergration by parts

anonymous · Answer

let x be u and sinx be dv

anonymous · Answer

formula is uv-int(v.du)

jamesj · Answer

Wait a second.  I think the question is
$$ \int x \sin^2 x \ dx $$ yes?

lgbasallote · Answer

wouldnt assigning u to sin^2(x) be easier? it's a little confusing integrating sin^2(x)...im just suggesting i dunno which is easier in the end..jsyk

anonymous · Answer

can you give me all serial solution

jamesj · Answer

The first thing to is to get rid of the sin^2 term.  Use a trig identity with cos(2x).

anonymous · Answer

standard trick is to write
what jamesj said

jamesj · Answer

cos(2x) = cos^2 x - sin^2 x
            = 1           - 2.sin^2 x

Thus sin^2 x = ....

anonymous · Answer

i couldnot solve it

jamesj · Answer

$$ \sin^2 x = \frac{1}{2} (1 - \cos 2x) $$
Hence
$$ \int x . \sin^2 x \ dx = \frac{1}{2} \int (x - x.\cos 2x) \ dx $$ 
See what to do now?

anonymous · Answer

go on

jamesj · Answer

So you don't know what to do next?  Surely you know how how to integrate the first part, 
$$ \int x \ dx $$ yes?  Now, for the second part, use integration by parts.

anonymous · Answer

thanks