Integral Calculator — Solve Definite and Indefinite Integrals (antiderivatives)

Calculator computes integrals of functions using various methods: basic integrals, u-substitution, integration by parts, partial fraction decomposition, trigonometric, hyperbolic, and logarithmic identities, algebraic manipulation of radicals, Euler substitution, standard integral forms, tangent half-angle substitution, and Ostrogradsky's method for rational functions. For definite integrals, the calculator applies the fundamental theorem of calculus.

Integrate with respect to

Upper limit	∫		+∞
Lower limit	∫		-∞

Loading content

The input recognizes various synonyms for functions such as asin, arsin, arcsin, sin^-1

Multiplication signs and parentheses are automatically added — for example 2sinx becomes 2*sin(x)

List of supported functions and constants:

• ln(x) — natural logarithm

• sin(x) — sine

• cos(x) — cosine

• tan(x) — tangent

• cot(x) — cotangent

• arcsin(x) — arcsine

• arccos(x) — arccosine

• arctan(x) — arctangent

• arccot(x) — arccotangent

• sinh(x) — hyperbolic sine

• cosh(x) — hyperbolic cosine

• tanh(x) — hyperbolic tangent

• coth(x) — hyperbolic cotangent

• sech(x) — hyperbolic secant

• csch(x) — hyperbolic cosecant

• arsinh(x) — inverse hyperbolic sine

• arcosh(x) — inverse hyperbolic cosine

• artanh(x) — inverse hyperbolic tangent

• arcoth(x) — inverse hyperbolic cotangent

• sec(x) — secant

• csc(x) — cosecant

• arcsec(x) — arcsecant

• arccsc(x) — arccosecant

• arsech(x) — inverse hyperbolic secant

• arcsch(x) — inverse hyperbolic cosecant

• |x|, abs(x) — absolute value

• sqrt(x), root(x) — square root

• exp(x) — \(e^x\)

• conj(z) — \(\overline{z}\)

• a+b — \(a+b\)

• a-b — \(a-b\)

• a*b — \(a\cdot b\)

• a/b — \(\dfrac{a}{b}\)

• a^b, a**b — \(a^b\)

• sqrt7(x) — \(\sqrt[7]{x}\)

• sqrt(n,x) — \(\sqrt[n]{x}\)

• lg(x) — \(\log_{10}\left(x\right)\)

• log3(x) — \(\log_3\left(x\right)\)

• log(a,x) — \(\log_a\left(x\right)\)

• ln^2(x), ln(x)^2 — \(\ln^2\left(x\right)\)

• y''', y'3 — \(y'''\)

• d^2y/dx^2, d2y/dx2 — \(\dfrac{\mathrm{d}^2y}{\mathrm{d}x^2}\)

• lambda — \(\lambda\)

• pi — \(\pi\)

alpha — \(\alpha\)

beta — \(\beta\)

• sigma — \(\sigma\)

gamma — \(\gamma\)

nu — \(\nu\)

• mu — \(\mu\)

phi — \(\phi\)

psi — \(\psi\)

• tau — \(\tau\)

eta — \(\eta\)

rho — \(\rho\)

• a123 — \(a_{123}\)

x_n — \(x_{n}\)

mu11 — \(\mu_{11}\)

• <= — \(\leq\)

>= — \(\geq\)

Bookmark this page — CTRL+D

Copy solution link

75% 90% 100% 110% 125% 🔍