Question

integral(-8(csc theta)^4)

Answer 1

\[-8 \int\limits(\csc \theta)^4 d \theta \]

Answer 2

I think the first step should be to split up (csctheta)^4

Answer 3

Do you remember think you know what it would be helpful to break it into?

Answer 4

it would be (csc theta)^2 * (csc theta)^2 I think

Answer 5

yea that's perfect because we know the integral of csc^2theta = -cot theta

Answer 6

but it is useless to have two so I would use a trig identity to make one of them into something else. Remeber csc^2theta = 1 + cot^2 theta

Answer 7

So what does that turn the problem into?

Answer 8

\[-8 \int\limits(\csc \theta)^2 +(\csc \theta)^2(\cot \theta)^2 d \theta\]

Answer 9

good you can make them into seperate integrals. csc^2 theta is a straight forward integral while for the other one you can use a substitution.

Answer 10

Don't forget about the -8

Answer 11

Could you confirm my answer?
I got \[4\sqrt{x^2 -4}+(2/3)\sqrt{x^2-4}\]

Answer 12

thats incorrect

Answer 13

oh well then.

Answer 14

where did you get sqrts from?

Answer 15

oh this was actually a trig substitution integration problem so I substituted the stuff back in. The answer with just the trig functions would be \[-8(-\cot \theta -(1/3)(\cot \theta)^3)\]

Answer 16

+C

Answer 17

The original problem was actually \[\int\limits (x^3/\sqrt{x^2-4})dx\]

Answer 18

\(\large \begin{align} \color{black}{\normalsize \text{i found a formula for this}\hspace{.33em}\\~\\
\int \csc^nx=\dfrac{\cos x\cdot \csc^{n-1} x}{n-1}+ \dfrac{n-2}{n-1}\int \csc^{n-2} x\,dx

}\end{align}\)

Answer 19

That's a not a formula I learned so I don't know if I am supposed to use that.

Answer 20

http://en.wikipedia.org/wiki/Integration_by_reduction_formulae

Answer 21

specially its for the power n

Answer 22

i see ur original question is diffferent