Integrating csc/cot^2. Help Needed

[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.

Homework Statement

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 ?

 

[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.

Let me know if you have any further questions about this.

 

[Fresh(2^)]

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.

Let me know if you have any further questions about this.

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.

 

[Forty-Two]

Glad I could help.