# Thread: Help with integral problem

1. ## Help with integral problem

Hi everyone! First post here of many to come. I have an integral problem that I'm not sure on how to work out.

$\displaystyle (integral of)sin^(4)xcosxdx$
(If someone could tell me how to input the various math symbols, that would be much appreciated)

The following are the answer choices:
$\displaystyle (A) .1sin^(5)xcos^(2)x + C$
$\displaystyle (B) .2sin^(5)x + C$
$\displaystyle (C) .2sin^(5)xcos^(2)x + C$
$\displaystyle (D) 4sin^(3)xcos^(2)x-sin^(5)x + C$
$\displaystyle (E) .2sin^(5)xcosx + sin^(5)x + C$

I'm pretty lost on what to do here. I can think of breaking up $\displaystyle sin^(4)x$ into $\displaystyle sin^(2)x * 1-cos^(2)x$. Other than that, I'm not sure how to go about this problem. Thanks for any replies!

2. Originally Posted by TheMathTham
Hi everyone! First post here of many to come. I have an integral problem that I'm not sure on how to work out.

$\displaystyle (integral of)sin^(4)xcosxdx$
(If someone could tell me how to input the various math symbols, that would be much appreciated)

The following are the answer choices:
$\displaystyle (A) .1sin^(5)xcos^(2)x + C$
$\displaystyle (B) .2sin^(5)x + C$
$\displaystyle (C) .2sin^(5)xcos^(2)x + C$
$\displaystyle (D) 4sin^(3)xcos^(2)x-sin^(5)x + C$
$\displaystyle (E) .2sin^(5)xcosx + sin^(5)x + C$

I'm pretty lost on what to do here. I can think of breaking up $\displaystyle sin^(4)x$ into $\displaystyle sin^(2)x * 1-cos^(2)x$. Other than that, I'm not sure how to go about this problem. Thanks for any replies!
let $\displaystyle u=\sin{x}$

3. is it sin(4x) or sin^4(x)?.
if it is sin^4(x) then u=sinx will do as von nemo said.
and if it is sin4x then we can use (sin(5x)-sin(3x))/2 in place of sin(4x).cos(x).
that should be integrable. hope this helps!!

4. Originally Posted by Pulock2009
is it sin(4x) or sin^4(x)?.
if it is sin^4(x) then u=sinx will do as von nemo said.
and if it is sin4x then we can use (sin(5x)-sin(3x))/2 in place of sin(4x).cos(x).
that should be integrable. hope this helps!!
Now that I've learned the proper way to use the math symbols:
$\displaystyle \int {sin^4}xcosxdx$

von nemo was right, u-substitution did work, and I got B as the answer. Thanks!

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