Question

integrate

(sin(x))^3

Answer 1

now you get to try to be a little clever

Answer 2

why don't I let you try it first and see how you approach it?

Answer 3

\[\int\limits \sin^2(x) \sin(x)\]
\[\frac{1}{2}\int\limits(1-\cos^2(x)) \sin(x)\]

Answer 4

where did the 1/2 come from?

Answer 5

I think you are mixing up trig identities

Answer 6

oh woops stupid lecture :P

Answer 7

1-cos(2x)/2?

Answer 8

it seems I could bring the 1/2 out in front?

Answer 9

half angle fomulas hmm and pytagorean formula... Seems you could use either...

Answer 10

I konfused myself :P

Answer 11

but one choice makes for a two-step problem and the other choice makes for a 3-step problem

Answer 12

ok so lets make it easy....

Answer 13

yes

Answer 14

\[\int\limits \sin(x)-\cos^2(x) \sin(x)dx :P\]

Answer 15

\[\int\limits \sin(x) dx- \int\limits \cos^2(x) \sin(x)dx\]
u = cos(dx)
du = -sin(x)dx

\[\int\limits \sin(x) dx--\int\limits u^2du\]

Answer 16

\[-\cos(x) + \frac{u^3}{3} + c\]

Answer 17

\[-\cos(x) + \frac{\cos(x)^3}{3} + c\]

Answer 18

Ok it's right WOOT!

Answer 19

Refer to the attachment.

Answer 20

hmm?

Answer 21

Hope you didn't do it all out all nice and put it into a tiff file... :P

Answer 22

Part of a screen capture from WolframAlpha.