Integral Calculator • With Steps!

Solve definite and indefinite integrals (antiderivatives) using this free online calculator. Step-by-step solution and graphs included! IntegralCalculator Calculateintegralsonline—withstepsandgraphing! AlsochecktheDerivativeCalculator!CalculadoradeIntegralesenespañolIntegralrechneraufDeutschКалькуляторИнтеграловнаРусском About Help Examples Options Practice TheIntegralCalculatorletsyoucalculateintegralsandantiderivativesoffunctionsonline—forfree!Ourcalculatorallowsyoutocheckyoursolutionstocalculusexercises.Ithelpsyoupracticebyshowingyouthefullworking(stepbystepintegration).Allcommonintegrationtechniquesandevenspecialfunctionsaresupported.TheIntegralCalculatorsupportsdefiniteandindefiniteintegrals(antiderivatives)aswellasintegratingfunctionswithmanyvariables.Youcanalsocheckyouranswers!Interactivegraphs/plotshelpvisualizeandbetterunderstandthefunctions.FormoreabouthowtousetheIntegralCalculator,goto"Help"ortakealookattheexamples.Andnow:Happyintegrating! EnterthefunctionyouwanttointegrateintotheIntegralCalculator.Skipthe"f(x)="partandthedifferential"dx"!TheIntegralCalculatorwillshowyouagraphicalversionofyourinputwhileyoutype.Makesurethatitshowsexactlywhatyouwant.Useparentheses,ifnecessary,e. g."a/(b+c)".In"Examples",youcanseewhichfunctionsaresupportedbytheIntegralCalculatorandhowtousethem.Whenyou'redoneenteringyourfunction,click"Go!",andtheIntegralCalculatorwillshowtheresultbelow.In"Options",youcansetthevariableofintegrationandtheintegrationbounds.Ifyoudon'tspecifythebounds,onlytheantiderivativewillbecomputed. ClickinganexampleentersitintotheIntegralCalculator.Movingthemouseoveritshowsthetext. $x^2-\frac{1}{3}y+0.7z$ $\alphax^2+\betax+\gamma$ $\frac{x}{x^2+1}$ $\operatorname{f}(x)\operatorname{f}'(x)$ $a_1x+K_\text{abc}$ $x^{-\frac{1}{3}}$ $\mathrm{e}^{1-x}$ $\sqrt{x}$ $\sqrt[3]{x+1}$ $\ln(x)$ $\log_{8}(x)$ $|x|$ $\sin(x)$ $\cos(x)$ $\tan(x)$ $\arcsin(x)$ $\arccos(x)$ $\arctan(x)$ $\sec(x)$ $\sinh(x)$ $\operatorname{arsinh}(x)$ $\operatorname{erf}(x)$ $\operatorname{B}(x,y)$ $\operatorname{\Gamma}(x)$ $\operatorname{Si}(x)$ $\mathrm{e}$ $\mathrm{\pi}$ $\mathrm{i}$ ConfiguretheIntegralCalculator: Variableofintegration: Upperbound(to):  +∞ Lowerbound(from):  –∞ Integratenumericallyonly? Simplifyexpressions? Simplifyallroots?(√x²becomesx,not|x|) Usecomplexdomain(ℂ)? Keepdecimals? Thepracticeproblemgeneratorallowsyoutogenerateasmanyrandomexercisesasyouwant.Youfindsomeconfigurationoptionsandaproposedproblembelow.Youcanacceptit(thenit'sinputintothecalculator)orgenerateanewone. Definiteintegrals Integrationbyparts Substitution Completingthesquare Polynomialsandpowers Exponentialfunctions Trigon./hyperb.functions Rationalfunctions Inv.trigon./hyperb.functions Logarithms Specialfunctions Trickyintegrals Acceptproblem  Nextproblem CalculatetheIntegralof…EnteryourownAnswer: Exit"checkanswer"mode CLR + – × ÷ ^ √ π ( ) Thiswillbecalculated: Loading…pleasewait!Thiswilltakeafewseconds. Notwhatyoumean?Useparentheses!Setintegrationvariableandboundsin"Options". RecommendthisWebsite Ifyoulikethiswebsite,thenpleasesupportitbygivingitaLike.Thankyou! ShareonFacebook BookRecommendation CalculusforDummies(2ndEdition)Anextremelywell-writtenbookforstudentstakingCalculusforthefirsttimeaswellasthosewhoneedarefresher.ThisbookmakesyourealizethatCalculusisn'tthattoughafterall.→ to the bookPaidlink.AsanAmazonAssociateIearnfromqualifyingpurchases. Support Donate Didthiscalculatorprovehelpfultoyou?ThenIwouldhighlyappreciateyoursupport.You'rewelcometomakeadonationviaPayPal. Result Above,enterthefunctiontointegrate.Variableofintegration,integrationboundsandmorecanbechangedin"Options".Click"Go!"tostarttheintegral/antiderivativecalculation.Theresultwillbeshownfurtherbelow. HowtheIntegralCalculatorWorks Forthosewithatechnicalbackground,thefollowingsectionexplainshowtheIntegralCalculatorworks.First,aparseranalyzesthemathematicalfunction.Ittransformsitintoaformthatisbetterunderstandablebyacomputer,namelyatree(seefigurebelow).Indoingthis,theIntegralCalculatorhastorespecttheorderofoperations.Aspecialtyinmathematicalexpressionsisthatthemultiplicationsigncanbeleftoutsometimes,forexamplewewrite"5x"insteadof"5*x".TheIntegralCalculatorhastodetectthesecasesandinsertthemultiplicationsign.TheparserisimplementedinJavaScript,basedontheShunting-yardalgorithm,andcanrundirectlyinthebrowser.ThisallowsforquickfeedbackwhiletypingbytransformingthetreeintoLaTeXcode.MathJaxtakescareofdisplayingitinthebrowser.Whenthe"Go!"buttonisclicked,theIntegralCalculatorsendsthemathematicalfunctionandthesettings(variableofintegrationandintegrationbounds)totheserver,whereitisanalyzedagain.Thistime,thefunctiongetstransformedintoaformthatcanbeunderstoodbythecomputeralgebrasystemMaxima.Maximatakescareofactuallycomputingtheintegralofthemathematicalfunction.Maxima'soutputistransformedtoLaTeXagainandisthenpresentedtotheuser.TheantiderivativeiscomputedusingtheRischalgorithm,whichishardtounderstandforhumans.That'swhyshowingthestepsofcalculationisverychallengingforintegrals.Inordertoshowthesteps,thecalculatorappliesthesameintegrationtechniquesthatahumanwouldapply.TheprogramthatdoesthishasbeendevelopedoverseveralyearsandiswritteninMaxima'sownprogramminglanguage.Itconsistsofmorethan17000linesofcode.Whentheintegrandmatchesaknownform,itappliesfixedrulestosolvetheintegral(e. g.partialfractiondecompositionforrationalfunctions,trigonometricsubstitutionforintegrandsinvolvingthesquarerootsofaquadraticpolynomialorintegrationbypartsforproductsofcertainfunctions).Otherwise,ittriesdifferentsubstitutionsandtransformationsuntileithertheintegralissolved,timerunsoutorthereisnothinglefttotry.Thecalculatorlacksthemathematicalintuitionthatisveryusefulforfindinganantiderivative,butontheotherhanditcantryalargenumberofpossibilitieswithinashortamountoftime.ThestepbystepantiderivativesareoftenmuchshorterandmoreelegantthanthosefoundbyMaxima.The"Check answer"featurehastosolvethedifficulttaskofdeterminingwhethertwomathematicalexpressionsareequivalent.TheirdifferenceiscomputedandsimplifiedasfaraspossibleusingMaxima.Forexample,thisinvolveswritingtrigonometric/hyperbolicfunctionsintheirexponentialforms.Ifitcanbeshownthatthedifferencesimplifiestozero,thetaskissolved.Otherwise,aprobabilisticalgorithmisappliedthatevaluatesandcomparesbothfunctionsatrandomlychosenplaces.Inthecaseofantiderivatives,theentireprocedureisrepeatedwitheachfunction'sderivative,sinceantiderivativesareallowedtodifferbyaconstant.Theinteractivefunctiongraphsarecomputedinthebrowseranddisplayedwithinacanvaselement(HTML5).Foreachfunctiontobegraphed,thecalculatorcreatesaJavaScriptfunction,whichisthenevaluatedinsmallstepsinordertodrawthegraph.Whilegraphing,singularities(e. g.poles)aredetectedandtreatedspecially.ThegesturecontrolisimplementedusingHammer.js.IfyouhaveanyquestionsorideasforimprovementstotheIntegralCalculator,don'thesitatetowritemeane-mail. ©DavidScherfgen2022—allrightsreserved. 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