Hello!(adsbygoogle = window.adsbygoogle || []).push({});

I would like to count (see the way how to count) this integral

[tex] \int_0^v \frac{1}{(1-v^2)^{3/2}} \,dv [/tex]

It should be

[tex]\frac{v}{\sqrt{1-v^2}}[/tex].

I have managed to count it (I have just derived the result, and followed steps in reversed order),

but this method was a little bit clumsy, I think.

It looked like this:

[tex]\int\frac{1}{(1-v^2)^{3/2}} \,dv=\int\frac{1-v^2+v^2}{(1-v^2)^{3/2}} \,dv=\int\left[\frac{1}{\sqrt{1-v^2}}+\frac{v^2}{(1-v^2)^{3/2}}\right]\,dv=[/tex]

[tex]=\frac{v}{\sqrt{1-v^2}}\ +\ C\ -\ \int\frac{v^2}{(1-v^2)^{3/2}}\,dv\ +\ \int\frac{v^2}{(1-v^2)^{3/2}}\,dv=\frac{v}{\sqrt{1-v^2}}\ +\ C[/tex]

so

[tex]\int_0^v \frac{1}{(1-v^2)^{3/2}} \,dv=\frac{v}{\sqrt{1-v^2}}\ +\ C\ -\ C\ =\frac{v}{\sqrt{1-v^2}}[/tex]

I would really appreciate if you write here some more elegant way (if exists) to count that integral.

I need to integrate it to get relativistic mass [tex]m_v=\frac{m_0}{\sqrt{1-v^2/c^2}}[/tex].

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Little help with integral

**Physics Forums | Science Articles, Homework Help, Discussion**