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Introduction to Indefinite Integrals - At A Glance:

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 x2, which is an inside function:

Sample Problem

We can't use substitution on

If we try to let u = x2 it just doesn't work, because we have an extra factor of x hanging around:

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