# find the primitive of cosec^2(x)

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• Sep 25th 2009, 06:13 PM
differentiate
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

Thanks in advance
• Sep 25th 2009, 06:35 PM
VonNemo19
Quote:

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

Thanks in advance

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

Does this make sense?
• Sep 25th 2009, 06:46 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, 06:48 PM
VonNemo19
Hey Calculus26, why don't you ever use latex?
• Sep 25th 2009, 11:07 PM
differentiate
Thanks guys