X xl5899 Mar 2014 909 2 malaysia Feb 29, 2016 #1 is it wrong to integrate dv / srt rt ( 1 +v^2) = ( (1+v^2)^0.5) / (2v)(0.5) ?

skeeter MHF Helper Jun 2008 16,217 6,765 North Texas Mar 1, 2016 #2 $\displaystyle \int \dfrac{dv}{\sqrt{1+v^2}}$ $v=\tan{t}$ $dv=\sec^2{t} \, dt$ $\displaystyle \int \dfrac{\sec^2{t}}{\sqrt{1+\tan^2{t}}} \, dt = \int \sec{t} \, dt = \ln|\sec{t}+\tan{t}|+C$ $\ln|\sqrt{1+v^2}+v|+C$ So, yes ... I'd say it's wrong. btw ... when are you going to learn latex and start posting something legible for a change?

$\displaystyle \int \dfrac{dv}{\sqrt{1+v^2}}$ $v=\tan{t}$ $dv=\sec^2{t} \, dt$ $\displaystyle \int \dfrac{\sec^2{t}}{\sqrt{1+\tan^2{t}}} \, dt = \int \sec{t} \, dt = \ln|\sec{t}+\tan{t}|+C$ $\ln|\sqrt{1+v^2}+v|+C$ So, yes ... I'd say it's wrong. btw ... when are you going to learn latex and start posting something legible for a change?