Question

Hello everyone, i've been attempting to solve this problem for over 10 minutes now no luck :(..

use a change of variable to solve for intergral of ..

(sin^4(x)-2sin^2(x)+sin(x)) * co(sx) dx

Answer 1

@nincompoop

Answer 2

try plug-in it in here https://www.mathway.com/

Answer 3

did you try sin^2x = u?

Answer 4

Yes I have still not working out for some reason

Answer 5

integration of products

Answer 6

u = sin^2(x)?
Don't you mean u should equal sin(x)?
That substitution seems like it would work.

Answer 7

I am with @iPwnBunnies let u = sin x, then everything is simple, you can solve it in 3 minutes

Answer 8

@OOOPS do you mind posting the solution?

Answer 9

Let u = sin x --> du = cos x dx
the integral becomes:
\[\int (u^4 -2u^2+u ) du= \dfrac{u^5}{5}-2\dfrac{u^3}{3}+\dfrac{u^2}{2}+C\]
replace u = sin x you get
\[\dfrac{sin^5(x)}{5}-2\dfrac{sin^3(x)}{3}+\dfrac{sin^2(x)}{2}+C\]

Answer 10

thank you I found my error

Answer 11

:)

Answer 12

Thanks @OOOPS! I appreciate it your help :D