MathSimplify
Calculus

Indefinite Integral Calculator

Find the antiderivative and indefinite integral of mathematical functions. Get instant step-by-step solutions — completely free, no signup required.

Free Indefinite Integral Calculator Calculator

Enter your problem below to get an instant step-by-step solution.

About Indefinite Integral Calculator

Find the antiderivative and indefinite integral of mathematical functions. Calculus is the mathematical study of continuous change. It provides tools for analyzing functions, computing areas and volumes, and solving differential equations that model real-world phenomena.

Our Indefinite Integral Calculator calculator handles every type of problem in this topic. Whether you are a student working through homework, preparing for an exam, or a professional needing a quick calculation, you can enter any indefinite integral calculator expression and receive a complete, verified solution with every step shown.

Indefinite Integral Calculator Formula

∫ xⁿ dx = xⁿ⁺¹ / (n + 1) + C, n ≠ −1

An indefinite integral (antiderivative) reverses differentiation. Because the derivative of any constant is zero, there is a whole family of antiderivatives, which is why every answer ends with “+ C”. Integrate term by term using the power rule and the standard integrals of eˣ, 1/x, sin and cos.

Worked Example

Find ∫ (6x² − 4x + 3) dx

  1. ∫ 6x² dx = 6 · x³/3 = 2x³
  2. ∫ −4x dx = −4 · x²/2 = −2x²
  3. ∫ 3 dx = 3x
  4. Add the constant of integration

Answer: 2x³ − 2x² + 3x + C

Common Mistakes to Avoid

  • Leaving out the + C.
  • Applying the power rule to x⁻¹ — ∫ 1/x dx = ln|x| + C.
  • Differentiating instead of integrating (multiplying by the power rather than dividing).

How to Use the Indefinite Integral Calculator Calculator

  1. 1

    Enter your calculus expression (e.g., a function for Indefinite Integral Calculator) into the input field

  2. 2

    Press Enter or click the Solve button to run the calculation

  3. 3

    Review the step-by-step solution that appears below the input

  4. 4

    Check the breakdown of each operation to understand the method

  5. 5

    Try a different problem to practice and build your understanding

Frequently Asked Questions

What is the Indefinite Integral Calculator formula?

∫ xⁿ dx = xⁿ⁺¹ / (n + 1) + C, n ≠ −1. An indefinite integral (antiderivative) reverses differentiation. Because the derivative of any constant is zero, there is a whole family of antiderivatives, which is why every answer ends with “+ C”. Integrate term by term using the power rule and the standard integrals of eˣ, 1/x, sin and cos.

Can you show a worked Indefinite Integral Calculator example?

Find ∫ (6x² − 4x + 3) dx: ∫ 6x² dx = 6 · x³/3 = 2x³; ∫ −4x dx = −4 · x²/2 = −2x²; ∫ 3 dx = 3x; Add the constant of integration. Answer: 2x³ − 2x² + 3x + C.

Is this Indefinite Integral Calculator calculator free to use?

Yes — the Indefinite Integral Calculator calculator on MathSimplify is completely free. There is no signup, no subscription, and no usage limit. Enter any problem and get the step-by-step solution instantly.

Can I use this for Indefinite Integral Calculator homework and exam practice?

Absolutely. The step-by-step breakdown is designed specifically for learning. You can use it to check your work, understand where you went wrong, or study the method before an exam. The calculator shows the full working, not just the final answer.

More Calculus Calculators

Related Math Tools

Expression Simplifier
Simplify any algebraic or calculus expression step-by-step.
Power Rule Calculator
Differentiate power functions instantly using the power rule.
Chain Rule Solver
Apply the chain rule to composite functions.