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Say we want to find

We can here see that we can use the method of substitution since the derivative of the inner function 3*x*^{2}+4 is *x*, except for a constant factor. We thus have

Thus gives us

Here we need to indicate that we still, in the end, will integrate over the interval *x*=1 to *x*=3 even if our variable, for the moment, is *x*. This we can do by writing *x*=1 as our lower integration limit.

We could also have calculated the new integration limits using the substitution *u*=3*x*^{2}+4.

I.e.

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