Calculus solver
Limits, derivatives, integrals, series and the applications built on them — with the rule named at each step, not just applied.
How to use it
- 1
Build the expression rather than typing it
Integrals, limits and nested fractions are where plain text falls apart. The formula editor draws the bounds where they belong and sends unambiguous LaTeX, which is the difference between the right integral and a plausible-looking wrong one.
- 2
Say what you want done
"Differentiate", "evaluate", "find the area between" and "does this converge" are four different questions about the same expression. Lead with the verb.
- 3
Check the rule it names
The first step says which rule is being applied — chain, parts, u-substitution, a series test. If that is not the rule your course wants you to practise, say so and ask again.
What it handles
Limits including one-sided limits, limits at infinity, the indeterminate forms and L'Hopital's rule, with the reason the form is indeterminate stated rather than assumed.
Derivatives by every standard rule — power, product, quotient, chain, implicit and logarithmic differentiation — plus the applications: critical points, concavity, optimisation, related rates and linear approximation.
Integrals by substitution, by parts, by partial fractions and by trigonometric substitution, definite and indefinite, plus areas, volumes of revolution, arc length and separable differential equations.
Sequences and series: the convergence tests, radius of convergence, and Taylor and Maclaurin expansions.
Where to double-check it
A long integration by parts is exactly where an arithmetic slip hides, because every subsequent line still looks reasonable. Differentiate the answer back — the solver does this in the check section for indefinite integrals, and it is worth reading.
Series questions are the strongest case for this tool, because the deliverable is the argument rather than a number: which test, why it applies, and what it does and does not tell you about the original series.
Rules it will name
| What you're looking at | Rule it will name | Example |
|---|---|---|
| A product of two functions | Product rule | x^2 sin(x) |
| A function inside another | Chain rule | (3x + 1)^5 |
| A quotient | Quotient rule, or rewrite as a product first | x / (x^2 + 1) |
| 0/0 or ∞/∞ in a limit | L'Hopital's rule | lim x→0 sin(x)/x |
| An integral with an inner derivative present | u-substitution | ∫ 2x e^(x^2) dx |
| A product under an integral | Integration by parts | ∫ x ln(x) dx |
| A rational function under an integral | Partial fractions | ∫ 1/(x^2 - 1) dx |
| Does a series converge? | Ratio, integral, comparison or alternating test | Σ 1/n^2 |
Calculus solver questions
- Does it do definite and indefinite integrals?
- Both. Indefinite answers carry the constant of integration, and definite ones show the evaluation at each bound rather than jumping to the difference.
- Can it handle implicit differentiation?
- Yes, and it keeps the dy/dx terms visible through the rearrangement instead of producing the final expression in one jump.
- Will it explain which series test to use?
- Yes. It names the test, says what about the terms made that test the right one, and states what the result does not prove — a divergence test that comes back inconclusive is reported as inconclusive.
- Is there a limit on how many problems I can do?
- There is no per-person limit and no account to run out of credits on. The site shares one daily AI allowance; on the rare day that runs out you are told so plainly, and it resets at midnight UTC.