Verified Calculus Solver with Step-by-Step Explanations

Integral Calculator with Steps

Calculate definite and indefinite integrals with explicit variables, bounds and the required integration constant.

Deterministic coreAnimated stepsNo sign-up to try

Dedicated workspace

Integral solver

Engine

Use ^ for powers and parentheses for functions. You can enter sec(x) and arctan(x) directly; trigonometric inputs use radians.

Input help and supported methods

Keep the original question visible. Confirm the variable and the live preview before calculating. Use ^(1/2) for a square root and explicit parentheses for function arguments.

Choose the integration variable. Leave both bounds empty for an antiderivative, or fill both for a definite integral. Supported improper integrals require a convergence rule; numerical approximations are not marked Verified.

Read the method

Try an example

Live problem preview

Choose the right workflow

Which integral workflow fits the problem?

Choose between an antiderivative, a bounded accumulated value, or algebraic preparation for a rational integrand.

IntegralsFind an antiderivative for an expression without finite bounds.
∫2 x dx\int 2\,x\,\mathrm{d}x
Use the calculator above
Definite integral calculatorUse lower and upper bounds to calculate accumulated change, without + C.
∫023 x2 dx\int_{0}^{2} 3\,x^{2}\,\mathrm{d}x
Open this calculatorPartial fraction calculatorDecompose a rational expression before integration; decomposition alone is not the integral.
3 x+5(x+1) (x+2)\frac{3\,x + 5}{\left(x + 1\right)\,\left(x + 2\right)}
Open this calculator

Rules you can recognize

How this calculator chooses a method

Power-rule antiderivatives

∫xn dx=xn+1n+1+C\int x^n\,\mathrm{d}x=\frac{x^{n+1}}{n+1}+C

For constant n ≠ −1, integrate x^n as x^(n+1)/(n+1) on a real interval where the expression is defined. The n = −1 case is ln|x|.

Linear substitution patterns

u=g(x)u=g(x)

Identify an inner expression together with its derivative factor, replace it with u, and integrate the simpler form.

Integration by parts guidance

∫u dv=uv−∫v du\int u\,\mathrm{d}v=uv-\int v\,\mathrm{d}u

Rearrange a product into u and dv so one factor becomes simpler after differentiation; supported cases show the resulting transformation.

Three clear moves

How to use this calculator

Leave both bounds empty for an indefinite integral and CalculusMate adds + C. Enter finite lower and upper bounds for a definite integral. Supported symbolic answers are checked by differentiation.

Enter one expression using standard mathematical syntax.

Choose the variable and task-specific options.

Review the result, verification note and ordered steps.

Verified means checked, not merely generated

Continue with a related calculator built for a different calculus intent.

Definite integral calculatorUse lower and upper bounds to calculate accumulated change, without + C.Partial fraction calculatorDecompose a rational expression before integration; decomposition alone is not the integral.DerivativesDifferentiate a single-variable expression or compute a higher-order derivative.LimitsEvaluate finite, infinite, or one-sided behavior near an approach value.