# Integrating xsinxcosxdx

1. Feb 11, 2009

### carlosgrahm

How do you integrate

xsinxcosxdx

2. Feb 11, 2009

### mathman

Inegrate by parts: u=x, dv=sinxcosxdx=sinxd(sinx)
You get x(sinx)2/2 -integral of (1/2)(sinx)2dx

You should be able to proceed (using double angle formula for cos to get rid of (sinx)2/2).

3. Feb 18, 2009

### Take_it_Easy

Since
2sin(x)cos(x) = sin(2x)
you can write the integrand function
$$x/2 \cdot \sin (2x)$$
you can use first the substitution
$$y=2x$$
and then use integration by part formula to integrate
$$y/4 \cdot \sin (y)$$
it is EASY if you choose to derive $$y/4$$ and integrate $$\sin(y)$$.

4. Feb 20, 2009

### maze

You can solve any question like this by expressing sin(x), cos(x), etc in terms of their exponential form and multiplying everything out.

cos(x) = [exp(ix)+exp(-ix)]/2
sin(x) = [exp(ix)-exp(-ix)]/(2i)