# Thread: Integral of cos^2(x)/sinx

1. ## Integral of cos^2(x)/sinx

Hi, I'm new here. I had a question on the thought process for this integral. I know what the answer is, I just don't see how to get to a certain step. The question is:

$\displaystyle \int \frac {cos^2x}{sinx}dx$

I checked the steps on wolframalpha, which said to rewrite the integral as:

$\displaystyle \int cos(x)cot(x)dx$

Okay, I understand that, but then it says to rewrite that integral as:

$\displaystyle \int csc(x) - sin(x)dx$

I don't understand this last step. Is there an identity that I'm not seeing? Any help is appreciated.

2. Originally Posted by Shananay
Hi, I'm new here. I had a question on the thought process for this integral. I know what the answer is, I just don't see how to get to a certain step. The question is:

$\displaystyle \int \frac {cos^2x}{sinx}dx$

I checked the steps on wolframalpha, which said to rewrite the integral as:

$\displaystyle \int cos(x)cot(x)dx$

Okay, I understand that, but then it says to rewrite that integral as:

$\displaystyle \int csc(x) - sin(x)dx$

I don't understand this last step. Is there an identity that I'm not seeing? Any help is appreciated.
I would ignore the first step.

$\displaystyle \frac{\cos ^2 x}{\sin{x}} = \frac{1-\sin ^2 x}{\sin{x}} = \frac{1}{\sin{x}} - \sin{x}$

3. Originally Posted by pomp
I would ignore the first step.

$\displaystyle \frac{\cos ^2 x}{\sin{x}} = \frac{1-\sin ^2 x}{\sin{x}} = \frac{1}{\sin{x}} - \sin{x}$
Ah perfect. Thank you.