Evaluate the following integral.

$cot(x)dx$

Solution

First $we$ write cotangent $in$ terms $ofsine$ and cosine.

$cot(x)dx$

$=$

$cos(x)$

$sin(x)$

$dx$

$.$

This suggests that $we$ should substitute

$u=sin(x),$

since then

$du=$

Incorrect: Your answer $is$ incorrect.

$dx,$

$sowe$ get the following. $(Rememberto$ use $absolute$ values where appropriate.$)$

$cot(x)dx$

$=$

$cos(x)$

$sin(x)$

$dx$

$=$

$du$

$u$

$=ln(|u|)+C$

$=$