TOPICS
Search

Integration by Substitution

Integration by substitution, also called u-substitution, is a method for evaluating an integral by reversing the chain rule. If u=g(x), then

intf(g(x))g^'(x)dx=intf(u)du.

For a definite integral, the limits must also be transformed, giving

int_a^bf(g(x))g^'(x)dx=int_(g(a))^(g(b))f(u)du.

More generally, the change of variables theorem specifies hypotheses ensuring that a change of variable preserves the value of an integral.

See also

Change of Variables Theorem, Integration by Parts

Explore with Wolfram|Alpha

References

Stewart, J. Calculus: Early Transcendentals, 7th ed. Belmont, CA: Brooks/Cole, 2012.

Cite this as:

Weisstein, Eric W. "Integration by Substitution." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/IntegrationbySubstitution.html

Subject classifications