What is Mathway Integral?
Mathway Integral is a powerful integral calculator that solves both definite and indefinite integrals with detailed step-by-step solutions. Whether you need to integrate polynomials, trigonometric functions, exponential functions, or complex expressions, Mathway Integral provides clear explanations for each step of the integration process. This is part of our comprehensive calculus solver suite.
Our integral calculator uses various integration techniques including substitution, integration by parts, partial fractions, and trigonometric substitution, automatically selecting the most appropriate method for your problem.
Types of Integrals Solved
Indefinite Integrals
Solve indefinite integrals (antiderivatives) without limits. Get the general solution plus the constant of integration.
Definite Integrals
Calculate definite integrals with upper and lower limits. Get the exact numerical value of the integral.
Multiple Integration
Solve double and triple integrals for multivariable calculus problems with step-by-step solutions.
Improper Integrals
Evaluate improper integrals with infinite limits or unbounded functions, checking for convergence.
Integration Techniques Supported
- U-Substitution: Change of variables to simplify integrals
- Integration by Parts: For products of functions using the formula ∫u dv = uv - ∫v du
- Partial Fractions: Decompose rational functions for easier integration
- Trigonometric Substitution: For integrals involving square roots of quadratic expressions
- Integration by Trigonometric Identities: Using trigonometric formulas to simplify integrals
- Tabular Integration: For repeated integration by parts
- Numerical Integration: For integrals that cannot be solved analytically
How to Use Mathway Integral Calculator
- Enter Your Integral: Type your integral using standard mathematical notation. For definite integrals, include the limits of integration.
- Select Calculus: Choose "Calculus" and then "Integral" from the menu options.
- Get Step-by-Step Solution: Mathway shows each step of the integration process, including which technique is used.
- Review the Solution: Understand the integration method and verify your work by reviewing each step.
Common Integral Examples
Mathway Integral can solve various types of integrals:
- Basic integrals: ∫x² dx = x³/3 + C
- Trigonometric integrals: ∫sin(x) dx = -cos(x) + C
- Exponential integrals: ∫e^x dx = e^x + C
- Definite integrals: ∫₀¹ x² dx = 1/3
- Integration by parts: ∫x·e^x dx
- Substitution: ∫2x·e^(x²) dx
- Partial fractions: ∫1/(x²-1) dx
- Improper integrals: ∫₁^∞ 1/x² dx
Benefits of Mathway Integral
- Multiple Techniques: Automatically applies the best integration method for your problem
- Detailed Steps: See every step of the integration process with clear explanations
- Handles Complex Integrals: Solves integrals that are difficult to compute manually
- Free to Use: Access core integral solving features at no cost
- Educational Value: Learn integration techniques by studying the step-by-step solutions
- Time Saving: Get solutions instantly instead of spending time on complex integrations
Frequently Asked Questions
Can Mathway solve definite and indefinite integrals?
Yes, Mathway Integral calculator can solve both definite integrals (with limits) and indefinite integrals (without limits), providing step-by-step solutions for each.
What integration techniques does Mathway use?
Mathway uses various integration techniques including u-substitution, integration by parts, partial fractions, trigonometric substitution, and other advanced methods.
Is the Mathway Integral calculator free?
Yes, Mathway Integral calculator offers free access to solve both definite and indefinite integrals with detailed step-by-step solutions.
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