Calculus Solver: Step-by-Step Derivatives, Integrals and Limits
- Free
- No sign-up
- Works on phones
- Shows the working
By Yasir Hafeez · Updated
This calculus solver works out derivatives, indefinite integrals, definite integrals and limits, and shows every step with the rule it used. Type a function, pick what you want to find, and press Solve step by step. It is free, needs no sign-up, and runs in your browser.
Use it to check homework, to see which rule applies at each line, or to get an answer you can follow rather than just copy.
What this calculus problem solver can do
- Derivative: first, second or third derivative of a function of \(x\), using the power, product, quotient and chain rules and the standard derivatives of trig, inverse trig, exponential, log and hyperbolic functions.
- Integral: the antiderivative (indefinite integral) with \(+C\), using integration rules, substitution and integration by parts where they apply.
- Definite: the value of \(\int_a^b f(x)\,dx\) between two bounds, including improper integrals with
infor-infas a bound. - Limit: \(\lim_{x\to c} f(x)\) as a two-sided limit or from the left or right, including limits at infinity and indeterminate forms solved with L’Hôpital’s rule.
Every result has a Copy result button and a Plot in Visual Lab button that graphs the function so you can see what the answer means.
How to use the solver
- Choose Derivative, Integral, Definite or Limit at the top of the solver.
- Type your function, for example
x^3 sin(x). A preview underneath shows how the solver read it. - Add the extra details the mode needs: the order of the derivative, the bounds \(a\) and \(b\) for a definite integral, or the point \(c\) and the side for a limit.
- Press Solve step by step. The answer appears first, followed by each step with the name of the rule used.
How to type functions
| You want | Type |
|---|---|
| Powers and roots | x^2, sqrt(x), cbrt(x) |
| Absolute value | |x| |
| Multiplication | 3x sin(2x) (no * needed) |
| Trig and inverse trig | sin cos tan sec csc cot, asin acos atan |
| Hyperbolic functions | sinh cosh tanh |
| Exponentials | e^x or exp(x) |
| Natural log | ln(x) (here log(x) also means the natural log) |
| Log base 10 | log10(x) |
| Constants and infinity | pi, e, inf, -inf |
Worked examples
1. Derivative with the product rule
For \(f(x) = x^3 \sin(x)\) the solver applies the product rule, then the power rule and the derivative of sine:
\[ \frac{d}{dx}\left[x^3 \sin(x)\right] = 3x^2 \sin(x) + x^3 \cos(x) \]
2. Integral by parts
For \(\int x e^x\,dx\), integration by parts with \(u = x\) and \(dv = e^x\,dx\) gives
\[ \int x e^x\,dx = x e^x - e^x + C \]
3. Improper definite integral
Choose Definite, type e^(-x), and set the bounds to 0 and inf:
\[ \int_0^{\infty} e^{-x}\,dx = 1 \]
4. Limit with L’Hôpital’s rule
Substituting \(x = 2\) into \(\dfrac{x^2 - 4}{x - 2}\) gives \(\tfrac{0}{0}\). The solver recognises the indeterminate form, applies L’Hôpital’s rule and finds
\[ \lim_{x\to 2} \frac{x^2 - 4}{x - 2} = 4 \]
Calculus solver or general math solver?
This solver is built for calculus: derivatives, integrals and limits. For algebra problems, use the dedicated tools instead: the quadratic formula calculator, the system of equations calculator, the polynomial roots calculator and the fraction calculator. The full list is on the calculators page.
Related calculators and guides
- Derivative calculator and second derivative calculator
- Integral calculator and definite integral calculator
- Limit calculator
- Rule guides: derivative rules, integration formulas and L’Hôpital’s rule
Frequently asked questions
Is this calculus solver free?
Yes. Every mode, including the step-by-step working, is free and needs no account.
Does it show the steps?
Yes. Each step is listed with the name of the rule applied, such as the chain rule, integration by parts or L’Hôpital’s rule, so you can follow the working line by line.
Can it solve improper integrals and limits at infinity?
Yes. Type inf or -inf as a bound in Definite mode, or as the point \(c\) in Limit mode.
What if it cannot find an exact answer?
Some functions have no antiderivative in elementary terms, such as \(e^{x^2}\). For those, use Definite mode to get a numerical value between two bounds.