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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 3x2+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=3x2+4.
I.e.
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