Integral Calculator
Solve indefinite and definite integrals step by step: substitution, by parts, partial fractions, improper limits and a shaded area plot.
Graph and area
Drag to pan, scroll or pinch to zoom, hover or tap a curve to trace it, click a gray point to pin its coordinates.
Step-by-step solution
About Integral Calculator
The integral calculator finds antiderivatives step by step with the methods taught in calculus courses: power rule, standard integrals, u-substitution, integration by parts (including the e^x sin x case), partial fractions with polynomial division, and trigonometric identities.
Every antiderivative is checked by differentiating it back before it is shown. When no rule applies, a full computer algebra engine is loaded on demand, and its answer is verified the same way.
For definite and improper integrals, with bounds such as 0 and pi or -inf and inf, the exact value is computed when possible and always confirmed by adaptive Gauss-Kronrod and tanh-sinh quadrature, with an error estimate. The graph shades the signed area.
How to use Integral Calculator
- Choose Indefinite or Definite.
- Type the function, for example x e^x or 1/(x^2 - 1). A trailing dx is optional.
- For a definite integral, enter the bounds: numbers, pi, e, inf or -inf.
- Read the result with + C, or the exact and decimal value of the definite integral.
- Open the steps to see each method used, and check the shaded area on the graph.