Question

integrate x^2(sin(2x)dx

Answer 1

there are two function, neither is the derivative of the other (x^2 can't come from the inner function 2x)

Proceed by Integration by Parts, taking care to pick the function that will eliminate itself through successive Integration by parts.

You've done IBP? are you familiar with LIATE?

Answer 2

yea i got x^2sin(2x)+4xcos(2x) + 4cos(2x) + C , not sure if its right though i used IBP twice and yea im familiar with Liate

Answer 3

it looks like your pulling your constants out backwards when integrating (ie
\[\int\limits_{}^{}\cos 2x= -\frac{1}{2}\sin 2x\]

as well can you write what youve subbed in the very first IBP

Answer 4

For parts
u = x^2
and dv = sin(2x)

Answer 5

\[u = x^2, v = -2\cos2x, du = 2x, dv = \sin2x\]

Answer 6

oh v = -1/2 cos 2x?

Answer 7

where did the -2 from v?

Answer 8

was thinking of derivative, thx for pointing that out

Answer 9

yeah, you got it now. no sweat