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i have a derivation of a physical equation, where there is an equation

$\int mv \gamma \,\textrm{d}v = \frac{m}{2}\int \gamma \, \textrm{d}(v^2)$

Q1: How did we derive right side from left one? Could anyone explain this step by step or provide me with names of the integration rules applied here so i can google it myself.

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$ \frac{dv^2}{dv}=2v \Rightarrow \frac{dv^2}2=vdv $

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    In fact sometimes it is easier to me to learn integration through diferentiation.2012-11-26
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This follows directly from

$\int A f(x)\, \text dx= A\int f(x)\, \text dx$

and a substitution.

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    @71GA $m$ is just a constant. Thus you can move it out of the integral.2012-11-26