What kinds of integrals can this calculator solve?

It solves indefinite and definite integrals of polynomials, rational functions of the form 1/(ax+b), trigonometric functions (sin, cos, tan, sec, csc, cot), hyperbolic functions, exponentials such as eˣ and aˣ, the natural logarithm ln(x), and any of the above with a linear inner argument (u-substitution with u = ax+b).

How do I enter a definite integral?

Open the Bounds panel under the keypad and type the lower and upper limits (numbers, π, e or simple expressions). The calculator will compute the antiderivative F(x) and then F(upper) − F(lower) automatically.

What does + C mean in the answer?

An indefinite integral has infinitely many antiderivatives that differ by a constant. The + C represents this arbitrary constant of integration. For definite integrals the constant cancels when you subtract F(lower) from F(upper).

Why does the calculator say a problem is not supported?

Some integrals require advanced techniques such as integration by parts on products like x·sin(x), trigonometric substitution, partial fractions for non-linear denominators, or series expansion. These are intentionally outside the scope of a step-by-step student tool. Try splitting the integrand into simpler terms or rewriting it before integrating.

∫ Kalkulus Integral-lommeregner

Beregn ubestemte og bestemte integraler trin for trin. Skriv integranden direkte eller brug det specialiserede tastatur til trig, log, eksponentielle og potensfunktioner.

Enter the integrand (use x as the variable)

x^2 + 3x - 5

Drikkepenges: powers need ^ — type x^2 for x² (bare x2 betyder x·2). Multiplikation er implicit — 2x, 3sin(x) og 5(x+1) virker alle. Brug sqrt(x) for √x, pi for π and e for Euler's number. The expression is treated as ∫ f(x) dx.

x² 3x² + 2x − 5 (2x+1)³ sin(x) cos(2x+1) eˣ e^(3x) 1/x ln(x) √x

Definite integral — optional

Nedre grænse a

Øvre grænse b

Leave both blank for the indefinite integral. Fill both to compute F(b) − F(a) and the numeric area under the curve.

Antiderivativer

About the Calculus Integral Lommeregner

The Calculus Integral Calculator finds the antiderivative of a function with respect to x and shows the working line by line. It is built for students, educators and self-learners who want to see why an answer is correct, not just the final result. Every step names the rule that was applied — power rule, sum rule, constant-multiple rule, u-substitution with a linear inner function, trigonometric rules, exponential rule or integration by parts — so you can match it back to your textbook or lecture notes.

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What is integration?

Integration is the reverse of differentiation. If F'(x) = f(x), then F(x) is called an antiderivative of f(x), written:

∫ f(x) dx = F(x) + C

The constant C represents the family of curves that all share the same derivative. For a definite integral with limits a and b, you evaluate the antiderivative at the bounds and subtract:

∫_a^b f(x) dx = F(b) − F(a)

Dette er Fundamental Theorem of Calculus og giver det fortegnede areal under kurven y = f(x) mellem x = a og x = b.

Standard integrationsregler

Constant rule: ∫ k dx = k·x + C
Power rule: ∫ xⁿ dx = xⁿ⁺¹/(n+1) + C, for n ≠ −1
Reciprocal rule: ∫ 1/x dx = ln|x| + C
Exponential rule: ∫ e^x dx = e^x + C and ∫ a^x dx = a^x/ln(a) + C
Sum / difference rule: ∫ [f(x) ± g(x)] dx = ∫ f(x) dx ± ∫ g(x) dx
Constant-multiple rule: ∫ k·f(x) dx = k · ∫ f(x) dx
Trig rules: ∫ sin(x) dx = −cos(x), ∫ cos(x) dx = sin(x), ∫ sec²(x) dx = tan(x)
u-substitution (linear inner): ∫ f(ax + b) dx = (1/a) · F(ax + b)
Integration by parts: ∫ ln(x) dx = x·ln(x) − x + C

How to use this calculator

Type or click your integrand ved hjælp af tastaturet ovenfor. Brug x som variablen, ^ til potenser og standardoperatorer.
Press Integrate. The big result panel shows the antiderivative with + C, plus a numbered breakdown of every rule applied.
(Optional) Open the Definite Integral panel og angiv den nedre og øvre grænse. Beregneren evaluerer F(b) − F(a) og viser det numeriske areal.
Try the example chips to see how common integrals are solved — polynomials, trig, exponentials, logarithms and reciprocals.

Common uses

GCSE Further Maths, A-Level Maths and IB HL homework
Leaving Certificate-kalkulus på højt niveau
First-year university calculus courses (engineering, physics, economics, computer science)
Hurtige kontrol af stamintegralerunder studier eller rettelse
Opbygning af intuition for kalkulus' fundamentalteorem

Ofte stillede spørgsmål

Why does my answer have a "+ C" at the end? Indefinite integrals are determined only up to an additive constant — any constant disappears under differentiation. The "+ C" is a reminder that infinitely many functions share the same derivative.

Can it integrate with respect to a variable other than x? Lommeregneren bruger x som variablen. Hvis dit problem bruger et andet bogstav, erstat det mentalt med x inden du indtaster. Strukturen af svaret er den samme.

How accurate is the numeric definite integral? Når en lukket form af antiderivat er fundet, evalueres F(b) − F(a) med dobbelt-præcisions flydende-komma-aritmetik, nøjagtig til ca. 12–13 decimaler. Når ingen lukket form er tilgængelig, falder lommeregneren tilbage til Simpson's rule med adaptiv underopdeling, som er nøjagtig til ca. 1×10⁻⁸ for glatte integrander.

Why does some integrand return "not supported"? Værktøjet fokuserer på standardreglerne fra indledende kalkulus: potens-, sum/difference-, konstant-ganget-, trigonometriske, eksponentielle, logaritmiske regler og u-substitution med en lineær indre funktion. Integraler, der kræver integration by parts af produkter som x·sin(x), trigonometrisk substitution, partialbrøknedbrydning på ikke-lineære nævnere, eller specielle funktioner er bevidst uden for dets rækkevidde. Prøv at opdele integranden i enklere led først, eller brug den relaterede Graphing Calculator til at visualisere arealet numerisk.

Does it handle constants like π and e? Ja. Skriv pi eller klik på π-tasten for π og e for Eulers tal. De behandles som nøjagtige konstanter i antiderivaet og konverteres til tal ved evaluering af bestemte grænser.

Can I use this for negative or fractional powers? Yes. The power rule works for any real n ≠ −1 — try x^(-2), x^(1/2) or sqrt(x).

Is my data stored anywhere? No. Every calculation runs locally in your browser and nothing is uploaded.

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Vigtig bemærkning: Dette værktøj er beregnet til at give estimater og trinvise uddannelsesforklaringer og bør ikke bruges som erstatning for professionel rådgivning. Oplysninger genereret af disse lommeregnere kan være ufuldstændige og tager ikke højde for alle individuelle omstændigheder. Søg altid rådgivning fra en certificeret ekspert (som en finansiel rådgiver, sundhedsperson eller licenseret ingeniør), inden du handler baseret på disse resultater.

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Calculus Derivative Calculator — Differentiate any function step-by-step. Power, product, quotient, chain, trig, exponential and log rules explained.
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