# Integrating csc/cot^2. Help Needed

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.

int csc/cot2

## 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 ?

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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.

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.