Integrating xcos(x)^2

[remote forum]

I don’t understand why my answer is incorrect. I can’t spot any inconsistencies or errors. Can you please explain why this is wrong?

[sacred sapphire]

Well, one thing I notice is that you forgot the constant of integration.

Also, 1/2 int cos(2x) dx = sin(2x)/4, not sin(4x)/4.

Here's how I worked it out:```
int xcos^2(x) dx = 1/2 int x + xcos(2x) dx
= x^2/4 + 1/2 int xcos(2x) dx

u = 2x
u/2 = x
1/2 du = dx

= x^2/4 + 1/8 int ucos(u) du
= x^2/4 + 1/8 * (usin(u) + cos(u)) + c
= x^2/4 + xsin(2x)/4 + cos(2x)/8 + c```

[remote forum]

I understand the way you've done it 🙂 thank you. I still don't understand why my method was incorrect though (excluding integrating cos(2x) to sin(4x).

[sacred sapphire]

Well, apart from that, which is, like, wrong enough on its own, like I said, you left off the constant of integration.

Oh, also!

You were supposed to integrate v du, but you didn't. You integrated dv du.

[remote forum]

Yes, thank you. This question was part of a larger mechanics question which provided limits. I wrote out the question neater to post on here and therefore didn't include the constant of integration.

[elfin creek]

@remote forum has given 1 rep to @sacred sapphire

[remote forum]

Fab! Thanks so much, could've been a bit less sassy though. I'm trying my best.

[sacred sapphire]

...where was I sassy?