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Calculus Solver

Calculus Solver with step-by-step solutions

Enter a function, choose what to do with it, and see the answer worked out rule by rule. Derivatives, integrals, limits, Taylor series and critical points are all solved for free, in your browser.

Operation
Your expression will be shown here as it will be read.

Solved entirely in your browser. Nothing you type is sent to a server or stored, and no account is needed.

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What this calculus solver does

This is a computer algebra tool built for learning calculus. It reads the function you type, applies the same rules you use on paper, and shows each one: the power rule, the chain rule, u-substitution, L'Hôpital's rule and the rest. You get more than the final answer; you can see exactly where it came from.

It is designed for high school, AP and college calculus students, for teachers preparing examples, and for anyone teaching themselves. All computation happens on your device, so it is fast, private and works without an account.

A curve with a tangent line at one point and the area under the curve shaded, the two central ideas of calculus

How to use the solver

  1. Choose an operation: derivative, indefinite or definite integral, limit, Taylor series, or critical points.
  2. Type your function using the syntax below, or tap Show keypad on a phone. Check the “Reads as” preview to confirm the solver understood you.
  3. Fill in any options: derivative order, integral bounds, the point a limit approaches, a Taylor center, or a search interval.
  4. Press Solve, then read the steps. Use Copy answer or Copy LaTeX to reuse the result, and Reset to start over.

How to type math expressions

The solver accepts ordinary calculator syntax. Multiplication signs are optional (2x, x sin x and (x+1)(x−1) all work), and symbols such as π, √ and ² can be pasted directly.

Expression syntax guide
Type thisMeaningShown as
x^2Powersx2x^{2}
3x or 3*xMultiplication (the * is optional)3x3x
(x+1)/(x-1)Fractions: wrap numerator and denominator in parenthesesx+1x−1\frac{x+1}{x-1}
sqrt(x), cbrt(x)Square and cube rootsx, x3\sqrt{x},\ \sqrt[3]{x}
x^(1/3)Fractional powersx1/3x^{1/3}
e^x or exp(x)Exponential functionexe^{x}
ln(x)Natural logarithm (log(x) is also read as ln)ln⁡x\ln x
log10(x), log(x, 2)Logarithms in other baseslog⁡10x, log⁡2x\log_{10}x,\ \log_{2}x
sin(x), cos(x), tan(x)Trig functions (also sec, csc, cot)sin⁡x\sin x
sin(x)^2 or sin^2(x)Powers of trig functionssin⁡2x\sin^{2}x
asin(x), atan(x)Inverse trig (arcsin, arccos and arctan also work)arcsin⁡x\arcsin x
abs(x) or |x|Absolute value∣x∣|x|
pi, eConstants π and eπ, e\pi,\ e
inf, -infInfinity, in bounds and limit points only∞\infty

Supported problem types

  • Derivatives

    ddx x2sin⁡x\frac{d}{dx}\,x^{2}\sin x

    Any order up to 10, with sum, product, quotient, power and chain rule steps.

  • Indefinite integrals

    ∫xex dx\int x e^{x}\,dx

    Standard forms, u-substitution, integration by parts and partial fractions, each answer verified.

  • Definite integrals

    ∫0∞e−x dx\int_{0}^{\infty} e^{-x}\,dx

    Exact values via the Fundamental Theorem of Calculus, improper integrals, and numerical values when needed.

  • Limits

    lim⁡x→0sin⁡xx\lim_{x\to 0}\frac{\sin x}{x}

    Two-sided, one-sided and at ±∞, using substitution, factoring and L'Hôpital's rule.

  • Taylor series

    ex≈1+x+x22e^{x} \approx 1 + x + \tfrac{x^{2}}{2}

    Taylor and Maclaurin polynomials up to order 10 about any center.

  • Critical points

    f′(x)=3x2−3f'(x) = 3x^{2} - 3

    Solve f′(x) = 0 or undefined, then classify as local max, min or neither.

How the solver computes results and steps

Your input is parsed into an expression tree and simplified with exact fractions, never rounded decimals. Derivatives are computed by applying one rule per node of that tree, which is why every step names a rule. Integrals are attempted with standard forms, substitution, integration by parts and partial fractions. Only if those fail is a bundled computer algebra system tried as a fallback.

Every answer is then checked independently. Antiderivatives are differentiated and compared with the integrand. Definite integrals are compared with high-accuracy numerical integration. Limits are confirmed by evaluating the function close to the point. If a check fails, the solver reports that it could not solve the problem rather than showing a doubtful answer.

Read the full methodology, including the numerical methods and their accuracy.

Worked examples

Example 1

Derivative

ddx(x2sin⁡x)\frac{d}{dx}\left(x^{2}\sin x\right)

  1. Product rule with f = x² and g = sin x.

    2xsin⁡x+x2cos⁡x2x\sin x + x^{2}\cos x

Answer

2xsin⁡x+x2cos⁡x2x\sin x + x^{2}\cos x

Example 2

Indefinite integral

∫x ex dx\int x\,e^{x}\,dx

  1. Integration by parts with u = x and dv = eˣ dx.

    xex−∫ex dxx e^{x} - \int e^{x}\,dx

Answer

xex−ex+Cx e^{x} - e^{x} + C

Example 3

Definite integral

∫0πsin⁡x dx\int_{0}^{\pi}\sin x\,dx

  1. An antiderivative is −cos x.

    [−cos⁡x]0π=−(−1)−(−1)\left[-\cos x\right]_{0}^{\pi} = -(-1) - (-1)

Answer

22

Example 4

Limit

lim⁡x→0sin⁡xx\lim_{x\to 0}\frac{\sin x}{x}

  1. Substitution gives 0/0, so apply L'Hôpital's rule.

    lim⁡x→0cos⁡x1=cos⁡0\lim_{x\to 0}\frac{\cos x}{1} = \cos 0

Answer

11

Common mistakes when entering expressions

  • 1/2x should be 1/(2x)

    Without parentheses, 1/2x means (1/2)·x. The preview shows how your input is read.

  • sin x^2 should be (sin(x))^2

    sin x^2 is read as sin(x²). Write sin(x)^2 or sin^2(x) for the square of sine.

  • e^2x should be e^(2x)

    The exponent stops at the first term: e^2x means e²·x. Wrap longer exponents in parentheses.

  • log(x) for base 10 should be log10(x)

    log(x) is the natural logarithm here, as in most computer algebra systems.

  • y = x^2 should be x^2

    Enter only the expression, not an equation.

  • sin^-1(x) should be asin(x)

    sin⁻¹ is ambiguous (inverse or reciprocal), so the solver asks you to choose.

Limitations

No solver handles everything, and this one tells you when it reaches its limits. It does not currently support:

  • Differential equations, multivariable calculus, vector calculus, or implicit differentiation.
  • Piecewise functions, floor and ceiling, factorials, or complex numbers.
  • Convergence tests for infinite series, or word problems.
  • Integrals without an elementary antiderivative, such as ∫ex² dx. The solver says so instead of guessing, and a definite integral still gets a numerical value.

Answers may also be written in a different but equivalent form from your textbook. For example, an antiderivative can differ from the book's by a constant. Always check important results; see the disclaimer.

Dedicated calculators and guides

Each calculator focuses on one operation and comes with its own rules, worked examples and common mistakes.

Frequently asked questions

Is this calculus solver free?

Yes. Every feature is free to use, with no account, no sign-up and no limit on the number of problems.

Does the solver show steps?

Yes. Derivatives and most integrals show every rule applied. Limits show substitution, factoring or L'Hôpital steps. Taylor polynomials show a table of derivatives and coefficients. When steps are not available (for example, an integral solved by the computer algebra fallback), the solver says so.

Is my input sent anywhere?

No. The math engine runs inside your browser. Your expressions are never uploaded, logged or stored, and once the page has loaded, solving does not need an internet connection.

How accurate are the answers?

Symbolic answers are exact, and each is checked independently: antiderivatives by differentiation, limits numerically, derivatives against finite differences. Numerical answers are labelled as such and are typically accurate to about 10 significant digits.

Can I use it for homework or exams?

Use it to learn and to check your own work. Follow your teacher's and school's rules: many courses do not allow calculators like this on graded assignments or exams.

What problems can't it solve?

Differential equations, multivariable calculus, implicit differentiation, series convergence tests and word problems are not supported. Some integrals have no elementary antiderivative, and the solver tells you when that is the case.

Start with a problem you're stuck on

Solve it yourself as far as you can, then let the solver show the remaining steps. Comparing the two is where the learning happens. When you're ready to go deeper, the study guides explain each technique from the ground up.

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