So, um, I am getting confused on integration problems where you have to do something with "a constant factor of n". Like, this example...(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\int\sqrt{1 + e^{4x^{3}}}e^{4x^{3}}x^{2}dx[/itex]

Then the example says to match it to the formula [itex]\int u^{n}du[/itex]

Okay... so it does that, but then... something I don't quite understand happens. It says that "du = [itex]e^{4x^{3}}(12x^{2})[/itex]" WAIT? WHERE DID THE 12 COME FROM? Then it says that "our integrand contains all of du except for the constant factor of 12" Then it does this...

[itex]\frac{1}{12}\int(1 + e^{4x^{3}})^{1/2} e^{4x^{3}}(12x^{2})dx[/itex]

Then it integrates like normal... but... WHERE DID THE 12 COME FROM? I don't know why, it just isn't obvious where this "constant factor of 12" came from?

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# This example is confusing me

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