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), csc(x), cot(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. Standard tan, cot, sec and csc integrals support affine inner arguments. Symbolic slopes must be nonzero; intervals must avoid poles.

Read the method

Try one. See the steps.

Click to fill the input. Calculation starts only when you choose Solve.

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.