Handling a constant

**polarbear73** · September 13th 2010, 11:22 AM

$dx/x=v^3dv/v^4+1$
After integration you get $\log x=(\log (v^4+1)/4)+c$
I think this yields $4\log x=\log (v^4+1)+4c$
Thus $\log x^4= \log (v^4+1)+4c$
I don't know how to handle the constant. Help?

**chisigma** · September 13th 2010, 12:08 PM

You have...

$\ln x^{4} = \ln (1+v^{4}) + 4\ c$ (1)

... that setting $4\ c = \ln \alpha^{4}$ and 'exponentiating' becomes...

$x = \alpha\ (1+v^{4})^{\frac{1}{4}}$ (2)

Kind regards

$\chi$ $\sigma$

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