integrate dv / srt rt ( 1 +v^2)

Mar 2014
909
2
malaysia
is it wrong to integrate dv / srt rt ( 1 +v^2) = ( (1+v^2)^0.5) / (2v)(0.5) ? IMG_20160301_153109[1].jpg
 

skeeter

MHF Helper
Jun 2008
16,217
6,765
North Texas
$\displaystyle \int \dfrac{dv}{\sqrt{1+v^2}}$

$v=\tan{t}$

$dv=\sec^2{t} \, dt$

$\displaystyle \int \dfrac{\sec^2{t}}{\sqrt{1+\tan^2{t}}} \, dt = \int \sec{t} \, dt = \ln|\sec{t}+\tan{t}|+C$

$\ln|\sqrt{1+v^2}+v|+C$


So, yes ... I'd say it's wrong.

btw ... when are you going to learn latex and start posting something legible for a change?