Indefinite Integral Calculator

Find antiderivatives for common calculus forms such as power functions, exponentials, sine, cosine, and reciprocal functions.

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Integral type

Coefficient a

Power n or rate k

Constant b for reciprocal

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What this calculator teaches

An indefinite integral finds a family of antiderivatives. The + C is important because many functions can have the same derivative.

This calculator covers common classroom forms and explains which integration rule is being used.

Formula & Symbols

Concept	Formula	Meaning
Power rule	`∫x^n dx = x^{n+1}/(n+1)+C`	Works when n ≠ -1.
Exponential rule	`∫e^{kx} dx = e^{kx}/k + C`	Divide by the inner derivative k.
Reciprocal rule	`∫1/u du = ln\|u\| + C`	Used when the denominator is linear.

Step-by-Step Examples

Example 1

Power rule

Integrate ∫3x² dx.
Add 1 to the power: 2 + 1 = 3.
Divide by the new power: 3x³/3.

✓ x³ + C.

Example 2

Exponential rule

Integrate ∫4e^{2x} dx.
The inner derivative is 2.
Divide the coefficient by 2.

✓ 2e^{2x} + C.

Where students use this

🎓

High school and college

Use the tool to check homework and understand each step.

📊

Data and modeling

Connect formulas to tables, graphs, and real values.

🧪

Science and engineering

Use math results inside physics, chemistry, and engineering problems.

💻

Computer science

Apply the same logic to algorithms, systems, and numerical work.

Common Mistakes to Avoid

⚠️

Forgetting + C

Indefinite integrals always need the constant of integration.

⚠️

Using power rule when n = -1

∫x⁻¹ dx is ln|x| + C, not x⁰/0.

⚠️

Forgetting chain-rule reversal

For e^(kx), sin(kx), or cos(kx), divide by k.

Frequently Asked Questions

What is an antiderivative? ▾

It is a function whose derivative gives the original function.

Why do we add C? ▾

Because constants disappear when differentiated, so the antiderivative is a family of functions.

Can this solve every integral? ▾

No. It focuses on common forms. Complex integrals may need substitution, parts, or numerical methods.

What is the difference between definite and indefinite integrals? ▾

Indefinite integrals produce a function plus C. Definite integrals produce a number over an interval.

Related Math Calculators

Formula Explorer connections

Interpretation: This formula measures limiting behavior, instantaneous change, accumulation or multivariable variation. Assumption: The function must satisfy the continuity or differentiability conditions required by the method. Check domains, bounds, orientation and singularities.

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