# Thread: find the primitive of cosec^2(x)

1. ## find the primitive of cosec^2(x)

Hey, can someone help me find the primitive of:

$\displaystyle cosec^2x$
the answer is $\displaystyle -cotx + c$

EDIT: $\displaystyle \int cosec^2 x$
$\displaystyle \int sec^2(90-x)$
$\displaystyle = tan(90-x)+ c$
$\displaystyle = cotx + c$

But how did they get - cotx

2. Originally Posted by differentiate Hey, can someone help me find the primitive of:

$\displaystyle cosec^2x$
the answer is $\displaystyle -cotx + c$

EDIT: $\displaystyle \int cosec^2 x$
$\displaystyle \int sec^2(90-x)$
$\displaystyle = tan(90-x)+ c$
$\displaystyle = cotx + c$

But how did they get - cotx

$\displaystyle \frac{d}{dx}[\cot{x}+C]=-\csc^2{x}\Rightarrow\int\csc^2{x}dx=-\cot{x}+C$

Does this make sense?

3. I agree completely with VonNemo however if you want to know why your method didn't work = -tan(pi/2 - x)

Since you would let u = pi/2 - x (use radians always in Calculus)

du = -dx

result follows

4. Hey Calculus26, why don't you ever use latex?

5. Thanks guys

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