Evaluate The Following Indefinite Integral Calculator

This calculator evaluates indefinite integrals using basic integration rules. Learn how to solve integrals step-by-step with our guide and examples.

How to Use This Calculator

To evaluate an indefinite integral:

Enter the integrand in the input field (e.g., "x^2 + 3x + 2")
Click "Calculate" to see the result
Review the step-by-step solution in the result panel

The calculator supports basic algebraic expressions and common functions like sin(x), cos(x), e^x, and ln(x).

Formula Used

The general form of an indefinite integral is:

∫f(x) dx = F(x) + C

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

For polynomial functions, we use the power rule:

∫x^n dx = (x^(n+1))/(n+1) + C, for n ≠ -1

For exponential functions, we use:

∫e^x dx = e^x + C

Worked Examples

Example 1: Polynomial Integral

Evaluate ∫(3x^2 + 2x + 1) dx

Apply the power rule to each term:
- ∫3x^2 dx = x^3 + C
- ∫2x dx = x^2 + C
- ∫1 dx = x + C
Combine the results: x^3 + x^2 + x + C

Example 2: Trigonometric Integral

Evaluate ∫sin(x) dx

The antiderivative of sin(x) is -cos(x) + C

Example 3: Exponential Integral

Evaluate ∫e^x dx

The antiderivative of e^x is e^x + C

Frequently Asked Questions

What is an indefinite integral?

An indefinite integral represents a family of functions that differ by a constant. It's written as ∫f(x) dx and represents all antiderivatives of f(x).

What is the constant of integration?

The constant of integration (C) accounts for the infinite number of antiderivatives that differ by a constant. It's necessary because differentiation removes constants.

Can this calculator handle all types of integrals?

This calculator handles basic algebraic, trigonometric, and exponential integrals. For more complex integrals, you may need symbolic computation software.