U-Substitution Integral Calculator

Master integration by substitution with ease. Enter your function and substitution to see step-by-step solutions.

Define Your Integral

Function f(x):

∫

Enter the function you want to integrate.

Substitution u = g(x):

Define u as a function of x for substitution.

Understanding U-Substitution

U-Substitution, or integration by substitution, is a method to simplify integrals when they are in the form ∫f(g(x))g'(x) dx. By setting u = g(x), the integral transforms into ∫f(u) du, which is often easier to solve.

This technique is the reverse of the chain rule in differentiation. The steps involve:

Choosing a suitable substitution u = g(x).
Finding du = g'(x) dx.
Rewriting the integral in terms of u.
Evaluating the new integral with respect to u.
Substituting back x in place of u to get the final result.

Use this calculator to effortlessly apply u-substitution. Input your function and substitution, and get detailed steps to understand the process and solution.

Learn More About U-Substitution