Integral Calculator - Step by Step Solutions

Advanced Integral Calculator

Calculate definite and indefinite integrals with step-by-step solutions and visual graphs

Function to Integrate Enter mathematical expressions using standard notation

Integral Type

Indefinite ∫f(x)dx

Definite ∫[a,b]f(x)dx

Lower Bound (a)

Upper Bound (b)

Click to compute the integral and show step-by-step solution

Enter a function above to see the integration steps and result

Function Visualization

Try These Examples

∫ x² dx

Power rule integration

∫ sin(x) dx

Trigonometric function

∫ eˣ dx

Exponential function

∫ 1/x dx

Natural logarithm

∫ x·eˣ dx

Integration by parts

∫ 1/(x²+1) dx

Inverse trigonometric

Frequently Asked Questions

How do I enter mathematical functions? +

Use standard mathematical notation:

• Powers: x^2, x^3, x^(-1)
• Trigonometric: sin(x), cos(x), tan(x)
• Exponential: e^x, exp(x)
• Logarithmic: ln(x), log(x)
• Fractions: 1/x, 1/(x^2+1)

What's the difference between definite and indefinite integrals? +

Indefinite integrals find the antiderivative (general form) and include a constant of integration (+C).

Definite integrals calculate the exact numerical value between two bounds and represent the area under the curve.

What integration techniques are supported? +

The calculator supports several integration methods:

• Power Rule: For polynomial functions like x², x³
• Basic Trigonometric: sin(x), cos(x) integration
• Exponential: e^x and related functions
• Integration by Parts: For products like x·e^x
• Logarithmic: Functions resulting in ln(x)
• Inverse Trigonometric: Functions like 1/(x²+1)

How accurate are the numerical results? +

For definite integrals, the calculator uses the trapezoidal rule with 1000 subdivisions, providing accuracy to about 6 decimal places for most smooth functions.

The step-by-step solutions show the exact analytical form when possible.

Can I integrate complex expressions? +

Currently, the calculator handles basic to intermediate functions. For complex expressions involving:

• Multiple variables
• Advanced trigonometric identities
• Partial fractions with complex denominators

Consider breaking them into simpler components or using the calculator as a learning tool for the techniques involved.

Why do I see a graph with my results? +

The graph helps visualize:

• Function behavior: See how your function looks
• Integration region: For definite integrals, the shaded area shows what's being calculated
• Bounds: Vertical dashed lines show integration limits

This visual representation makes it easier to understand the geometric meaning of integration.

What if I get an error message? +

Common issues and solutions:

• Syntax errors: Check your function notation (use * for multiplication, ^ for powers)
• Undefined functions: Make sure you're using supported functions
• Division by zero: Avoid bounds that make denominators zero
• Complex results: Some functions may not have elementary antiderivatives

Try the provided examples to see correct formatting.