Use integration by parts to find

Hint

You will need to use integration by parts twice!

Answer

We want *u'* to be simpler than *u*, so choose

*u* = *x*^{2}

*v'* = sin *x*

Then

*u'* = 2*x*

*v* = -cos *x*

We use the formula for integration by parts:

Now we need to go figure out

This requires integration by parts again.

Take

*u* = *x*

v' = cos *x*

Then

*u'* = 1

*v* = sin *x*

Applying the integration by parts formula,

Now that we know

we can go pick up where we left off. We don't bother including the + *C* in the parentheses, since having +* C* instead of + 2*C* doesn't change the final answer.