Integral with substitution including variable itself(t=tx)

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From the thread about the Gaussian integral,

Bryan Yocks set $~~t=xt$ for $ \int^1 _0 e^{-x^2 t^2} dt$ and got $ \frac{1}{x} \int^x _0 e^{-t^2}dt $

But I can’t figure out why $dt$ changed to $\frac{1}{x} dt$.

How can it be done like this?

Thank you in advance.