Evaluate The Indefinite Integral Calculator

Indefinite integrals are fundamental to calculus and have applications in physics, engineering, and economics. This calculator helps you evaluate indefinite integrals quickly and accurately.

What is an Indefinite Integral?

An indefinite integral represents the antiderivative of a function. Unlike definite integrals, which calculate the area under a curve between two points, indefinite integrals find all possible antiderivatives of a function.

The general form of an indefinite integral is written as:

∫f(x) dx = F(x) + C

where F(x) is the antiderivative of f(x), and C is the constant of integration.

How to Use This Calculator

Enter the function you want to integrate in the input field.
Select the variable of integration (usually x).
Click "Calculate" to evaluate the integral.
Review the result and the step-by-step solution.

This calculator supports basic algebraic functions. For more complex functions, consult calculus textbooks or advanced software.

Basic Integration Rules

Here are some fundamental integration rules:

∫xⁿ dx = (xⁿ⁺¹)/(n+1) + C (for n ≠ -1)
∫eˣ dx = eˣ + C
∫sin(x) dx = -cos(x) + C
∫cos(x) dx = sin(x) + C
∫1/x dx = ln|x| + C

These rules form the basis for evaluating many common indefinite integrals.

Example Calculations

Let's evaluate the integral of x²:

∫x² dx = (x³)/3 + C

This result shows that the antiderivative of x² is (x³)/3 plus an arbitrary constant C.

Common Mistakes to Avoid

Forgetting the constant of integration (C)
Incorrectly applying the power rule (remember to add 1 to the exponent)
Miscounting the coefficients in polynomial functions
Confusing indefinite and definite integrals

Frequently Asked Questions

What is the difference between definite and indefinite integrals?

Definite integrals calculate the area under a curve between two points, while indefinite integrals find all possible antiderivatives of a function.

Why is the constant of integration important?

The constant of integration (C) accounts for the infinite number of possible solutions to an indefinite integral, as any constant added to an antiderivative will also be an antiderivative.

Can this calculator handle trigonometric functions?

Yes, this calculator supports basic trigonometric functions like sine and cosine.