I have to integrate $\displaystyle 2dx/sin(x)^2$. The calculator gave me the answer of $\displaystyle -2/tan(x)$, but I'm not sure how to get there.
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Which the derivative of cotan(x) ?
Yes. How do you integrate sin(x)^2 into tan(x)? Do you have to substitute something?
note that $\displaystyle \frac{2}{\sin^2{x}} = 2\csc^2{x}$
Originally Posted by skeeter note that $\displaystyle \frac{2}{\sin^2{x}} = 2\csc^2{x}$ But how does that turn into 2/tan(x)? wouldn't it just be 2tan(x)?
Originally Posted by Nacho Which the derivative of cotan(x) ? $\displaystyle \left( {\cot x} \right)^\prime = - \csc ^2 x \Rightarrow \cot x = - \int {\csc ^2 xdx} \Leftrightarrow \frac{2} {{\tan x}} = - \int {\frac{2} {{\sin ^2 x}}dx} $
Okay. I get it now. There are two substitutions. Once to get csc from sin and another time to get tan from cot. Thank you.
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