# Integrating csc/cot^2. Help Needed

1. Mar 23, 2010

### Fresh(2^)

Hey guys working on a problem for an assignment but my algebra is weak regrettably and I need some assistance.

Note:: I left the x and dx out for clarity.

1. The problem statement, all variables and given/known data

int csc/cot2

3. The attempt at a solution

int csc x/cot2x dx= int csc/cos2/sin2
= int cscsin2/cos2
= int 1/sin * sin2/cos2
= int sin/cos2

Is the algebra at the equal signs correct? If not what went wrong?

Then I make a u -substitution u = cos x then du = -sinx dx then dx = - du/sinx

that makes - int 1/u2du then i just replace that u with x

Correct ?

Last edited: Mar 23, 2010
2. Mar 23, 2010

### Forty-Two

Everything is you've done looks great up to when you get

$$-\int\frac{1}{u^{2}}du$$

from there you integrate with respect to u.

Once you arrive at answer to this integral, you then substitute cos(x) back into the problem for u.

3. Mar 23, 2010

### Fresh(2^)

Thanks no other questions. I could finish easily with 1/cos + K

EDIT: - int 1/u^2 = - int u ^ -2 = - ( - 1 / u) = 1/u since u = cos then 1/ cos + K follows.

Last edited: Mar 23, 2010
4. Mar 23, 2010