FreeMathHelp.com's Integral Calculator

Compute Integrals Step-by-Step

This new calculator from FreeMathHelp.com will walk you through computing integrals step-by-step. Enter any function and we'll show you how to find its integral (antiderivative) using appropriate integration techniques.

Enter a function to integrate:

Type naturally or click in the box to use the math keyboard. For integrals, use \int for ∫. Examples: \int x^2 dx or \int_{0}^{1} x^2 dx for definite integrals.

\int_{0}^{1} x^2 \, dx

LaTeX:

How does it work?

Enter your function in the box above and click the button to submit. The calculator will identify which integration technique to apply (power rule, substitution, integration by parts, partial fractions, etc.) and show you the step-by-step process. For definite integrals, include the bounds and we'll evaluate the result. Remember the idea is to *learn* -- not to copy solutions blindly. Don't rely on any one tool to do all the work for you, and always check your work for correctness!

Try finding integrals of:

\int x^2 dx (power rule)
\int \sin(x) dx (basic trig)
\int e^x dx (exponential)
\int \frac{1}{x} dx (natural log)
\int_{0}^{1} x^2 dx (definite integral)
\int 2x \cdot e^{x^2} dx (substitution)

Common Integration Techniques

Here's a quick reference of integration methods this calculator uses:

Power Rule: ∫x^n dx = x^(n+1)/(n+1) + C (where n ≠ -1)
Substitution: Replace u = g(x) to simplify the integral
Integration by Parts: ∫u dv = uv - ∫v du
Partial Fractions: Break rational functions into simpler fractions
Trigonometric Substitution: For expressions with √(a² - x²), etc.

Tips for Using the Calculator