Integral Calculator
Find the indefinite integral of standard and polynomial functions, or an accurate definite integral between two limits. The formula used is shown step by step below the answer, and is included when you save as PDF or image. A general symbolic engine is not possible in the browser, so unusual integrands fall back to a precise numerical value in definite mode.
Integral
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How to type your function
^ | power, e.g. x^2 is x squared |
* | multiply, e.g. 3*x (write the star) |
/ | divide, e.g. 1/x |
sqrt(x) | square root |
sin(x) cos(x) tan(x) | trigonometric functions (radians) |
e^x or exp(x) | exponential |
ln(x) log(x) | natural log, log base 10 |
pi, e | constants 3.14159..., 2.71828... |
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How it works
Key forms: ∫xⁿ dx = xⁿ⁺¹/(n+1) for n ≠ -1, ∫x⁻¹ dx = ln|x|, ∫sin x dx = -cos x, ∫cos x dx = sin x, ∫eˣ dx = eˣ. Definite integrals use Simpson's rule.Frequently Asked Questions
Which integrals can it solve exactly?
Polynomials and standard forms (powers, 1/x, sin, cos, e^x, sqrt) are integrated exactly for the indefinite case. Other forms are handled numerically in definite mode.
How accurate is the definite integral?
It uses Simpson's rule with 1000 intervals, which is very accurate for smooth functions. Sharp spikes or discontinuities can reduce accuracy.
Why no full symbolic integration?
Full symbolic integration needs a computer algebra system running on a server. This tool works entirely in your browser, so it covers the common exact forms and uses accurate numerical methods for the rest.