# Math Help - cot integral

1. ## cot integral

Hi,

Can someone help me with the integral Cot/sq. 1+2sinx, please?

I tried doing u substitution

I set u=1+sinx
du=2cosx

Will this work or should I try integration by parts?

I also know that cot=1/tan

Thank you

2. Originally Posted by chocolatelover
Hi,

Can someone help me with the integral Cot/sq. 1+2sinx, please?

I tried doing u substitution

I set u=1+sinx
du=2cosx

Will this work or should I try integration by parts?

I also know that cot=1/tan

Thank you
you cannot have cot by itself, you have to have cot(something). please type your question properly

3. Sorry

Cotx/sq. 1+2sinx

4. $\displaystyle\int\frac{\cot x}{(1+2\sin x)^2}dx=\int\frac{\cos x}{\sin x(1+2\sin x)^2}dx$
Substitute $\sin x=u$.

5. I'm trying to integrate "Cotx/sq. 1+2sinx"

Thank you

6. Originally Posted by chocolatelover
Sorry

Cotx/sq. 1+2sinx
and by that i suppose you mean $\frac {\cot x}{\sqrt{1 + 2sin(x)}}$ ?

parentheses are important too. change cot(x) into cos(x)/sin(x), then make the substitution $u = \sqrt {1 + 2 \sin x}$

7. Would the final answer be 1/2ln sq. 1+2sinx+c

I did:

(1/2) int du/sq. u dx=
1/2 int. 1/sq. u dx
1/2 int. ln|sq. u|+c=
1/2 ln sq. 1+2sinx+c

Thank you

8. Originally Posted by chocolatelover
Would the final answer be 1/2ln sq. 1+2sinx+c

I did:

(1/2) int du/sq. u dx=
1/2 int. 1/sq. u dx
1/2 int. ln|sq. u|+c=
1/2 ln sq. 1+2sinx+c

Thank you
please read my instructions in my last post, and use parentheses to clarify what you mean

9. Originally Posted by chocolatelover
Can someone help me with the integral Cot/sq. 1+2sinx, please?
Does this make sense?

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10. Originally Posted by Krizalid
Does this make sense?

¬¬
Hey, it's the same question (asked by the same person). I saw that thread but i didn't remember it, since i never posted in it. i made the same substitution as you did