In calculus, integration by substitution — popularly called u-substituion or simply the substitution method — is a technique of integration whereby a complicated looking integrand is rewritten into a simpler form by using a change of variables:
- , where .
In the case of a definite integral,
- , where , .
Consider the integral:
By letting , thus (since ), and observing that , the integral simplifies to
which is easily integrated to obtain:
Note that this integral can also be done using integration by parts, although the final answer may look different because of the different steps involved.