Calculus AI: Calculus Problem Solver with Steps

Calculus AI that explains, not just answers. Type a derivative, integral or limit — or photograph it — and Sumzo works through it step by step, naming each rule it uses, from the power rule to integration by parts.

Tip: use the math keyboard for symbols like √, x² and fractions. You can also attach a photo, screenshot or PDF of the problem (up to 4 files).

What should Sumzo do?
Try an example:
Explanation

Math keyboard

Keys go in at the cursor. Select part of your problem first to wrap it — for example, select x + 1 and press √.

How to use the calculus solver

  1. Type the problem, or pick Derivative, Integral or Limit and type just the function. Use ^ for powers and the math keyboard for √, π and fractions.
  2. For a definite integral, give the limits: “from 0 to 2”. For a limit, give the value: “as x → 2”.
  3. Press Solve. Each step names the rule — power, product, chain, substitution — and the answer comes first.
  4. Ask “Why?” about any step, or switch to Simple for a gentler explanation.

Worked examples

Easy: a derivative with the power rule

  1. Differentiate x3−5x2+2xx^3 - 5x^2 + 2x term by term: ddxxn=nxn−1\frac{d}{dx}x^n = nx^{n-1}.
  2. 3x2−10x+23x^2 - 10x + 2.

Medium: a definite integral

  1. Integrate 3x2+13x^2 + 1: an antiderivative is x3+xx^3 + x.
  2. Evaluate from 0 to 2: (8+2)−(0+0)=10(8 + 2) - (0 + 0) = 10.
  3. So ∫02(3x2+1) dx=10\int_0^2 (3x^2 + 1)\,dx = 10.

Hard: a limit of the form 0/0

  1. Substituting x=2x = 2 into x2−4x−2\frac{x^2 - 4}{x - 2} gives 00\frac{0}{0}, so simplify first.
  2. Factor: (x−2)(x+2)x−2=x+2\frac{(x - 2)(x + 2)}{x - 2} = x + 2 for x≠2x \neq 2.
  3. Now substitute: lim⁡x→2(x+2)=4\lim_{x \to 2} (x + 2) = 4.

Common calculus mistakes

  • Forgetting the +C+ C on an indefinite integral.
  • Using the power rule on a product: ddx(xsin⁡x)\frac{d}{dx}(x \sin x) needs the product rule.
  • Missing the chain rule: ddx(3x+1)4=12(3x+1)3\frac{d}{dx}(3x + 1)^4 = 12(3x + 1)^3, not 4(3x+1)34(3x + 1)^3.
  • Substituting into a limit that gives 00\frac{0}{0} and stopping there — simplify first.

Frequently asked questions

Is there an AI for calculus that shows the steps?

Yes — Sumzo AI solves calculus problems typed in words or symbols, or from a photo, and explains every step. For polynomials, the derivative and integral calculators also work exactly with Sumzo’s math engine.

Can this calculus problem solver do precalculus too?

Yes: functions, logarithms, trigonometry and limits as well as derivatives and integrals. For a single formula, the dedicated calculators are often quicker.

How accurate is the calculus AI?

Answers Sumzo’s math engine can calculate are checked by the engine; others come from Sumzo AI and say whether they were checked. Read the working, and check derivatives by differentiating your integral back.

Is the calculus solver free?

Yes. You can solve problems without an account; an account only saves your history.