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Step-by-step calculus

Integral Solver

Enter the integrand, choose the variable and optional limits, and get the integral with the method explained step by step.

Works in your browserSteps explainedVideo explanations

Learn the method

Integration, one decision at a time

Start by asking whether you need a family of antiderivatives or a value over an interval.

∫xn dx=xn+1n+1+C(n≠−1)\int x^n\,dx=\frac{x^{n+1}}{n+1}+C\quad(n\ne-1)
Calculus formulas

Worked example

  1. 1For ∫ x eˣ dx, choose u=x and dv=eˣ dx.
  2. 2Integration by parts gives x eˣ − ∫ eˣ dx.
  3. 3The answer is eˣ(x−1)+C. Differentiating it gives x eˣ.

A definite integral measures signed accumulation, not always geometric area. Split at sign changes when the question asks for total area.

What this integral solver does

  • Indefinite integrals with the constant of integration and the conditions under which the result holds
  • Definite and improper integrals with the limits you set; convergence is checked and explained
  • Names the technique used: substitution, integration by parts, partial fractions, trigonometric identities
  • Numeric verification: antiderivatives are differentiated back, definite integrals are integrated numerically

How to use it

  1. Type the integrand. Use ^ for powers, sqrt(), e^x, ln(x), or insert a formula with the Σ editor.
  2. Pick the variable of integration and switch to Definite to enter the lower and upper limits (∞ is allowed).
  3. Press Solve to see the answer, the steps and the shaded area on the graph.

Questions about the integral solver

Does the integral solver show steps?

Yes. Every integral is solved with numbered steps that name the technique used and show the expression after each transformation.

Can it compute definite and improper integrals?

Yes. Switch to Definite and enter the bounds. Infinite bounds are allowed; the solver states whether the integral converges and verifies finite values numerically.

What if the integral has no elementary antiderivative?

The solver tells you so instead of inventing an answer, and explains what can be done instead, such as a definite value or a series.

Why is there a + C in the answer?

An indefinite integral is a family of functions that differ by a constant. The solver shows + C and explains it in the steps.