# Math Help - More fun conceptual stuff :(

1. ## More fun conceptual stuff :(

Given $cos(x)= \frac{1-u^2}{1+u^2}$ then

$u^2$=

sin(x)= u

dx=

2. Originally Posted by Selim
Given $cos(x)= \frac{1-u^2}{1+u^2}$ then

$u^2=\frac{1-cos(x)}{1+cos(x)}$

$sin(x)=\frac{2u}{1+u^2}$

$dx=\frac{2\,du}{1+u^2}$
$u=\frac{sin(x)}{1+cos(x)}=tan({\frac{x}{2}})$

These are the substitutions that were used for $\int\frac{1}{3+2cos(x)}\,dx$