# Integration by Substitution

Use substitution when the integrand can be factored into something with an "inside function" *u* and something that's more-or-less the derivative of *u* (if the constant coefficients don't quite agree, that's ok).

### Sample Problem

We would use integration by substitution on

because *x* is a constant multiple of the derivative of *x*^{2}, which is an inside function:

### Sample Problem

We can't use substitution on

If we try to let *u* = *x*^{2} it just doesn't work, because we have an extra factor of *x* hanging around:

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