# find the primitive of cosec^2(x)

• Sep 25th 2009, 07:13 PM
differentiate
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

• Sep 25th 2009, 07:35 PM
VonNemo19
Quote:

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?
• Sep 25th 2009, 07:46 PM
Calculus26
I agree completely with VonNemo however if you want to know why your method didn't work

http://www.mathhelpforum.com/math-he...31b739b6-1.gif = -tan(pi/2 - x)

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

du = -dx

result follows
• Sep 25th 2009, 07:48 PM
VonNemo19
Hey Calculus26, why don't you ever use latex?
• Sep 26th 2009, 12:07 AM
differentiate
Thanks guys