Integral calculator

How to use the integral calculator

Type the function with x as the variable and press "Integrate" to get the antiderivative, written as F(x) + C. For a definite integral, tick the box and enter the limits. Write it the way you would in class: x^2 for powers, e^(3x), ln(x), sqrt(x), sin(x)^2 or sin^2(x), arctan(x). Use a point for decimals (0.5).

Before showing you an antiderivative we differentiate it and compare the result with your function at several points. If they don't match, you don't see it. For definite integrals we also check that the function is continuous on the interval and compute the value numerically a second way, so the Fundamental Theorem of Calculus answer, F(b) − F(a), is backed up by an independent number.

Examples worked out with this calculator

• Basic antiderivative: $\int \frac{1}{1+x^2}\,dx = \arctan x + C$ and $\int_0^1 \frac{1}{1+x^2}\,dx = \frac{\pi}{4} \approx 0.7854$
• Integration by parts: $\int x\,e^x\,dx = e^x\,(x-1) + C$
• Partial fractions: $\int \frac{3x+2}{x^2+x-2}\,dx = \frac{4\ln|x+2|}{3} + \frac{5\ln|x-1|}{3} + C$

The calculator shows the answer, not the working. If your homework asks for the method (which u to pick in a u-substitution, how to split into partial fractions), the step-by-step button sends the problem to PhotoExamAI. To check an antiderivative by hand, differentiate it with the derivative calculator: you should get back the function you started with. More free calculators are in the study tools section.