Question

how do you solve for the antiderivative of
x(sinx)^3?

Answer 1

rewrite (sinx)^3 as Sinx*(Sinx)^2.. then use trig identities and integration by parts

Answer 2

can you help me out with that

Answer 3

Too much to type, click on show steps:
http://www.wolframalpha.com/input/?i=Integrate+%28x%28sinx%29%5E3%29
if u get lost at a step, I'll explain

Answer 4

you get
xsinx[1/2(1-cos(2x))] or xinx(1-(cosx)^2)

Answer 5

i just want to know which step do you take and what is the next move after either one of these steps

Answer 6

It doesn't really matter, you could solve this both ways, but i think the first one is easier..

Answer 7

sure

Answer 8

xsinx[1/2(1-cos(2x))] now pull out the half:
(1/2) Integral (xSinx-xSinxCos(2x))

Answer 9

yup

Answer 10

Then split the integral into two:
(1/2) { Integral (xSinx) - Integral (xSinxCos(2x))) }

Answer 11

The first integral is easy, it's just integration by parts, u = x, dv = Sinxdx

Answer 12

ya the first one is fine but the other one, what do you do?

Answer 13

for the second one use more trig identities: SinA*CosB = (1/2)(Sin(a-b)+Sin(a+b))

Answer 14

that is not a typical trig identity. that is why i wanted to know if anyone else knew how to do this, it was one of our problem sets, but my teacher couldnt even give me an answer or tell me about the procedure.

Answer 15

it isn't, i've just seen too many of these integrals..

Answer 16

lol, maybe