Question

Evaluate :
$\int \frac{\frac{1}{2}}{1+t}\Rightarrow \frac{1}{2}\ln \left(1+t\right)$

Answer 1

$\frac{1/2}{(1+t)}\Rightarrow \frac{1}{2}ln(1+t)$

LHS

$I=\int \frac{1/2}{(1+t)}dt$

put $1+t=p0$

$\Rightarrow dt=dp$

$\to I=\int \frac{1/2dp}{p}=\int \frac{1}{2}\left(\frac{dp}{p}\right)$

$=\frac{1}{2}\left(n/p\right)$

$I=\frac{1}{2}\left(n\right)|1+t|$

$\therefore \int \frac{1/2}{(1+t)}dt=\frac{1}{2}ln|1+t|$