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Prove that convolution in linear time invariant systems is commutative.

I'm trying to show that $\int_{-\infty}^{\infty}x(\tau)h(t-\tau)d\tau = \int_{-\infty}^{\infty}x(t - \tau)h(\tau)d\tau $ but I think I may be misunderstanding something.

By change of variables for integration, I let $u=t-\tau$ and therefore with the limits of integration $u(-\infty) = t - (-\infty) = \infty$ and $u(\infty) = t - (\infty) = -\infty$.

And I get $-\int_{-\infty}^{\infty}x(t - u)h(u)du$. But this seems like the appropriate way to change variables, am I missing something here?

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    If $u = t - \tau$, then $du= -dt$, right? – 2017-01-23

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You are on the right path, but you forget to change the $d\tau$. we have $$u=t-\tau$$ which implies $$du=-d\tau $$ Voila!