# Antiderivative Calculator

> Free Step-by-Step Integral Solver & Calculus Guides


## Posts

- [Antiderivative of tan x: −ln|cos x| + C, Derived Step by Step](https://antiderivativecalculator.com/antiderivative-of-tanx/): The antiderivative of tan x is −ln|cos x| + C, or ln|sec x| + C. See two proofs, why the absolute value matters, tan² x, tan³ x and arctan x.
- [Antiderivative of cos x: sin x + C (Plus cos 2x, cos² x and More)](https://antiderivativecalculator.com/antiderivative-of-cosx/): The antiderivative of cos x is sin x + C. See three quick proofs, then work up from cos 2x to cos² x, cos³ x, x cos x and e^x cos x, with practice.
- [7 Common Antiderivative Mistakes (and How to Fix Them)](https://antiderivativecalculator.com/antiderivative-mistakes/): Spot and fix the 7 most common antiderivative mistakes, from forgetting + C to fake chain rules, with wrong vs correct work and a quick self-test.
- [How to Study Calculus on Your Own: A Roadmap With Checkpoints](https://antiderivativecalculator.com/how-to-study-calculus/): Learn calculus on your own with a 5-stage roadmap, a prerequisite quiz, checkpoint tests, a weekly schedule and the study loop that actually works.
- [Why Is Integration So Hard? 6 Reasons and How to Fix Each One](https://antiderivativecalculator.com/why-is-integration-so-hard/): Why is integration harder than differentiation? See 6 real reasons, a self-diagnosis table, and the order that makes integration much easier to learn.
- [Definite vs Indefinite Integral: The Difference, Explained Simply](https://antiderivativecalculator.com/definite-vs-indefinite-integral/): What is the difference between a definite and an indefinite integral? See a side-by-side table, one function done both ways, signed area and examples.
- [What Is Calculus Used For in Real Life? 6 Examples With Math](https://antiderivativecalculator.com/what-is-calculus-used-for-in-real-life/): See how calculus is used in real life, in medicine, driving, business, engineering, AI and biology, with a small worked example for each one.
- [10 Antiderivative Practice Problems With Step-by-Step Solutions](https://antiderivativecalculator.com/antiderivative-practice-problems/): Practice antiderivatives with 10 problems in three levels, from basic rules to integration by parts, each with a hint, a full solution and a score guide.
- [Antiderivative of e^x (Plus e^2x, e^-x and x e^x)](https://antiderivativecalculator.com/antiderivative-of-ex/): The antiderivative of e^x is e^x + C. Learn why, then work through e^2x, e^-x, e^(3x+1), x e^x and 2^x, and see why e^(x²) has no formula.
- [Antiderivative of 1/x: Why It Is ln|x| + C](https://antiderivativecalculator.com/antiderivative-of-1-x/): The antiderivative of 1/x is ln|x| + C. Learn why the power rule fails, why the absolute value matters, how 1/x² is different, and see worked examples.
- [Antiderivative of ln x: x ln x − x + C, Step by Step](https://antiderivativecalculator.com/antiderivative-of-lnx/): The antiderivative of ln x is x ln x − x + C. See the integration by parts trick, a quick check, and the integrals of ln(2x), (ln x)², ln x/x and log x.
- [Antiderivative of sin x: Answer, Proof and Examples](https://antiderivativecalculator.com/antiderivative-of-sinx/): The antiderivative of sin x is −cos x + C. See why the minus sign appears, a memory trick, the antiderivative of cos x, and sin 2x, sin²x and x sin x.
- [Best Free Antiderivative Calculators Compared (With a 5-Problem Test)](https://antiderivativecalculator.com/best-free-online-antiderivative-calculators/): Compare Wolfram|Alpha, Symbolab, Integral-Calculator.com, GeoGebra, Desmos and more, then test any tool yourself with 5 integrals.
- [How to Check an Antiderivative: 4 Easy Methods](https://antiderivativecalculator.com/how-to-check-your-antiderivative-answer/): Check any antiderivative in seconds: differentiate it, plug in numbers, compare different-looking answers, or read the graph. Worked examples included.
- [Can a Calculator Do Integrals? Which Ones Can Find Antiderivatives](https://antiderivativecalculator.com/can-a-calculator-solve-antiderivatives/): Which calculators can find antiderivatives? Compare TI-84, TI-89, TI-Nspire CAS, HP Prime and online tools, and see which integrals no calculator can do.
- [Should Students Use Antiderivative Calculators? Pros, Cons and Rules](https://antiderivativecalculator.com/why-students-use-antiderivative-calculators/): Why do students use antiderivative calculators, and is it cheating? See the benefits, the risks, and 5 rules for learning with a calculator.
- [How to Use an Antiderivative Calculator: A Step-by-Step Tutorial](https://antiderivativecalculator.com/how-to-use-an-antiderivative-calculator/): Learn to use an antiderivative calculator: how to type functions, read the answer and steps, check the result, and fix the most common input errors.
- [Antiderivative of Exponential Functions: a^x, 2^x, 10^x and More](https://antiderivativecalculator.com/antiderivative-of-exponential-functions/): The antiderivative of a^x is a^x/ln a + C. See where ln a comes from, work through 2^x, 10^x, (1/2)^x and a^(kx), and solve a real growth problem.
- [Antiderivatives of Trig Functions: sin, cos, tan, sec, csc, cot](https://antiderivativecalculator.com/antiderivative-of-trigonometric-functions/): Antiderivatives of all six trig functions, sin, cos, tan, cot, sec and csc, with a short proof for each, plus sec², sin², tan² and worked examples.
- [Integration by Parts: Formula, LIATE Rule and 8 Examples](https://antiderivativecalculator.com/integration-by-parts/): Learn the integration by parts formula, how to choose u with LIATE, the tabular method, and 8 worked examples with answers you can check.
- [U-Substitution: How to Do It, With 5 Patterns and Examples](https://antiderivativecalculator.com/u-substitution/): Learn how to do u-substitution step by step. Spot the 5 patterns that tell you what u should be, handle definite integrals, and practice with answers.
- [Power Rule for Integration: 5 Levels From Easy to Tricky](https://antiderivativecalculator.com/power-rule-for-antiderivatives/): The power rule for integration: add 1 to the exponent and divide. Learn it in 5 levels, including negative powers, roots and fractions, with practice.
- [Antiderivative Rules and Formulas: The Complete Cheat Sheet](https://antiderivativecalculator.com/antiderivative-rules/): Every antiderivative rule and formula in one place: power, exponential, log, trig and inverse trig rules, with examples and the rules that do not exist.
- [Constant of Integration: What Is C in Integration (and How to Find It)](https://antiderivativecalculator.com/constant-of-integration/): C in integration is the constant of integration. See why we add + C, why the integral of a constant is kx + C, and how to find C from a starting value.
- [How to Find the Antiderivative: An 8-Question Checklist](https://antiderivativecalculator.com/how-to-find-the-antiderivative/): Learn how to find the antiderivative of any function with an 8-question checklist that tells you which method to use, with an example for each step.
- [Antiderivative vs Derivative: The Difference, Side by Side](https://antiderivativecalculator.com/antiderivative-vs-derivative/): Derivatives find rates; antiderivatives find the function behind a rate. Compare them side by side, rule by rule, with a motion example you can picture.
- [What Is an Antiderivative? A Simple Guide for Beginners](https://antiderivativecalculator.com/what-is-an-antiderivative/): An antiderivative undoes a derivative. Learn what it means in simple words, why we add + C, how to read the notation, and try a short quiz.

## Pages

- [Calculus Glossary](https://antiderivativecalculator.com/calculus-glossary/): What is this glossary?
- [Jacobian Calculator](https://antiderivativecalculator.com/jacobian-calculator/): What is the Jacobian?
- [Instantaneous Rate of Change Calculator](https://antiderivativecalculator.com/instantaneous-rate-of-change-calculator/): What is the instantaneous rate of change?
- [Exponential Growth Calculator](https://antiderivativecalculator.com/exponential-growth-calculator/): What is the exponential growth formula?
- [Acceleration Calculator](https://antiderivativecalculator.com/acceleration-calculator/): How do you calculate acceleration?
- [Concavity Calculator](https://antiderivativecalculator.com/concavity-calculator/): How do you find where a function is concave up or down?
- [Lagrange Multiplier Calculator](https://antiderivativecalculator.com/lagrange-multiplier-calculator/): What is the Lagrange multiplier method?
- [Differential Equation Solver](https://antiderivativecalculator.com/differential-equation-solver/): How does this differential equation solver work?
- [Curl Calculator](https://antiderivativecalculator.com/curl-calculator/): How do you calculate the curl of a vector field?
- [Wronskian Calculator](https://antiderivativecalculator.com/wronskian-calculator/): What is the Wronskian?
- [Matrix Calculator](https://antiderivativecalculator.com/matrix-calculator/): What can this matrix calculator do?
- [Determinant Calculator](https://antiderivativecalculator.com/determinant-calculator/): How do you find the determinant of a matrix?
- [Cross Product Calculator](https://antiderivativecalculator.com/cross-product-calculator/): How do you find a cross product?
- [Eigenvalue and Eigenvector Calculator](https://antiderivativecalculator.com/eigenvalue-calculator/): How do you find eigenvalues and eigenvectors?
- [Euler's Method Calculator](https://antiderivativecalculator.com/eulers-method-calculator/): What is Euler’s method?
- [Laplace Transform Calculator](https://antiderivativecalculator.com/laplace-transform-calculator/): What is the Laplace transform?
- [Interval of Convergence Calculator](https://antiderivativecalculator.com/interval-of-convergence-calculator/): How do you find the interval of convergence?
- [Linear Approximation Calculator](https://antiderivativecalculator.com/linear-approximation-calculator/): What is linear approximation?
- [Asymptote Calculator](https://antiderivativecalculator.com/asymptote-calculator/): How do you find asymptotes?
- [Partial Fraction Decomposition Calculator](https://antiderivativecalculator.com/partial-fraction-decomposition-calculator/): What is partial fraction decomposition?
- [Simplify Calculator](https://antiderivativecalculator.com/simplify-calculator/): What does it mean to simplify an expression?
- [Quadratic Formula Calculator](https://antiderivativecalculator.com/quadratic-formula-calculator/): What is the quadratic formula?
- [Factoring Calculator](https://antiderivativecalculator.com/factoring-calculator/): What does a factoring calculator do?
- [Calculus Guides](https://antiderivativecalculator.com/blog/)
- [Free Calculus Calculators](https://antiderivativecalculator.com/calculators/): Every calculator below is free, shows a full step-by-step solution, and checks its own answer. Pick a tool to get started.
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- [Limit Calculator](https://antiderivativecalculator.com/limit-calculator/): This free limit calculator finds limits step by step. It tries direct substitution first.
- [Partial Derivative Calculator](https://antiderivativecalculator.com/partial-derivative-calculator/): This partial derivative calculator differentiates functions of two or three variables, such as \(f(x, y) = x^2y + \sin(xy)\).
- [Second Derivative Calculator](https://antiderivativecalculator.com/second-derivative-calculator/): This second derivative calculator finds \(f''(x)\) step by step. It shows the first derivative, then differentiates again.
- [Derivative Calculator](https://antiderivativecalculator.com/derivative-calculator/): This free derivative calculator finds the derivative of any function and shows each step.
- [Triple Integral Calculator](https://antiderivativecalculator.com/triple-integral-calculator/): This triple integral calculator evaluates \(\iiint f(x,y,z)\,dV\) one layer at a time. You enter the function and three sets of limits.
- [Double Integral Calculator](https://antiderivativecalculator.com/double-integral-calculator/): This double integral calculator evaluates \(\iint f(x,y)\,dA\) step by step. Enter the function and the limits for the inner and outer integral.
- [Integration by Parts Calculator](https://antiderivativecalculator.com/integration-by-parts-calculator/): This integration by parts calculator solves integrals of products, like \(x e^x\), \(x^2\sin x\), and \(x\ln x\).
- [U-Substitution Calculator](https://antiderivativecalculator.com/u-substitution-calculator/): This u-substitution calculator solves integrals by substitution and shows exactly how.
- [Improper Integral Calculator](https://antiderivativecalculator.com/improper-integral-calculator/): Use this improper integral calculator to find out if an integral converges (has a finite value) or diverges (grows without end).
- [Definite Integral Calculator](https://antiderivativecalculator.com/definite-integral-calculator/): This definite integral calculator finds the value of \(\int_a^b f(x)\,dx\) and shows how to get it.
- [Integral Calculator](https://antiderivativecalculator.com/integral-calculator/): This free integral calculator solves indefinite and definite integrals and shows every step.
- [Contact Us](https://antiderivativecalculator.com/contact-us/): Have a question, found a mistake, or want a new calculator? Send us a message with the form below.
- [About Us](https://antiderivativecalculator.com/about-us/): We are a free calculus learning site.
- [Privacy Policy](https://antiderivativecalculator.com/privacy-policy/): Our calculators run in your browser. The functions you type are not sent to our server. We use Google Analytics to count visits, and it uses cookies.
- [Antiderivative Calculator](https://antiderivativecalculator.com/): Type any function and get its antiderivative in seconds. You see every step in plain English, and each answer is checked by taking its derivative.


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