# Math Help - find the primitive of cosec^2(x)

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

Hey, can someone help me find the primitive of:

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

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

But how did they get - cotx

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

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

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

But how did they get - cotx

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

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