integrals.wolfram.comIntegral Calculator: Integrate with Wolfram|Alpha

Uh oh! Wolfram|Alpha doesn’t run without JavaScript. Please enable JavaScript. If you don’t know how, you can find instructions here . Once you’ve done that, refresh this page to start using Wolfram|Alpha. WolframAlpha Online Integral Calculator Solve integrals with Wolfram|Alpha x s i n x 2 d x Math Input Natural Language Math Input More than just an online integral solver Wolfram|Alpha is a great tool for calculating antiderivatives and definite integrals, double and triple integrals, and improper integrals. The Wolfram|Alpha Integral Calculator also shows plots, alternate forms and other relevant information to enhance your mathematical intuition. Learn more about: Integrals Tips for entering queries Use Math Input above or enter your integral calculator queries using plain English. To avoid ambiguous queries, make sure to use parentheses where necessary. Here are some examples illustrating how to ask for an integral using plain English. integrate x/(x-1) integrate x sin(x^2) integrate x sqrt(1-sqrt(x)) integrate x/(x+1)^3 from 0 to infinity integrate 1/(cos(x)+2) from 0 to 2pi integrate x^2 sin y dx dy, x=0 to 1, y=0 to pi View more examples Access instant learning tools Get immediate feedback and guidance with step-by-step solutions for integrals and Wolfram Problem Generator Learn more about: Step-by-step solutions Wolfram Problem Generator VIEW ALL CALCULATORS BMI Calculator Dilution Calculator Mortgage Calculator Interest Calculator Loan Calculator Present Value Calculator Car Payment Calculator Future Value Calculator Limit Calculator Derivative Calculator Double Integral Calculator Triple Integral Calculator Series Expansion Calculator Discontinuity Calculator Domain and Range Calculator Factoring Calculator Quadratic Formula Calculator Equation Solver Calculator Partial Fraction Decomposition Calculator System of Equations Calculator Determinant Calculator Eigenvalue Calculator Matrix Inverse Calculator What are integrals? Integration is an important tool in calculus that can give an antiderivative or represent area under a curve. The indefinite integral of , denoted , is defined to be the antiderivative of . In other words, the derivative of is . Since the derivative of a constant is 0, indefinite integrals are defined only up to an arbitrary constant. For example, , since the derivative of is . The definite integral of from to , denoted , is defined to be the signed area between and the axis, from to . Both types of integrals are tied together by the fundamental theorem of calculus. This states that if is continuous on and is its continuous indefinite integral, then . This means . Sometimes an approximation to a definite integral is desired. A common way to do so is to place thin rectangles under the curve and add the signed areas together. Wolfram|Alpha can solve a broad range of integrals How Wolfram|Alpha calculates integrals Wolfram|Alpha computes integrals differently than people. It calls Mathematica’s Integrate function, which represents a huge amount of mathematical and computational research. Integrate does not do integrals the way people do. Instead, it uses powerful, general algorithms that often involve very sophisticated math. There are a couple of approaches that it most commonly takes. One involves working out the general form for an integral, then differentiating this form and solving equations to match undetermined symbolic parameters. Even for quite simple integrands, the equations generated in this way can be highly complex and require Mathematica’s strong algebraic computation capabilities to solve. Another approach that Mathematica uses in working out integrals is to convert them to generalized hypergeometric functions, then use collections of relations about these highly general mathematical functions. While these powerful algorithms give Wolfram|Alpha the ability to compute integrals very quickly and handle a wide array of special functions, understanding how a human would integrate is important too. As a result, Wolfram|Alpha also has algorithms to perform integrations step by step. These use completely different integration techniques that mimic the way humans would approach an integral. This includes integration by substitution, integration by parts, trigonometric substitution and integration by partial fractions. Pro Mobile Apps Products Business API & Developer Solutions LLM Solutions Resources & Tools About Contact Connect © 2024 Wolfram Alpha LLC Terms Privacy wolfram.com Wolfram Language Mathematica Wolfram Demonstrations Wolfram for Education...