Rewrite Integral Calculator

This rewrite integral calculator helps you transform complex integrals into simpler forms using algebraic, trigonometric, and other techniques. The calculator provides step-by-step solutions and explains the rewriting process.

How to Use This Calculator

To use the rewrite integral calculator:

Enter the integral expression you want to rewrite in the input field.
Select the rewriting technique from the dropdown menu.
Click "Calculate" to see the rewritten integral and step-by-step solution.
Review the result and use it in your calculations or further analysis.

The calculator supports common integral rewriting techniques including substitution, integration by parts, and trigonometric identities.

Formula Used

General Integral Rewriting

The rewrite integral calculator uses algebraic manipulation and integral identities to transform integrals. The exact formula depends on the specific technique selected.

For substitution, the calculator uses:

∫f(x)dx = ∫f(g(u)) * g'(u)du

Where x = g(u) and dx = g'(u)du.

The calculator applies the appropriate technique based on the input integral and selected method.

Worked Examples

Example 1: Basic Substitution

Original integral: ∫x√(x² + 1) dx

Let u = x² + 1, then du = 2x dx and x dx = du/2.

Rewritten integral: (1/2)∫u^(1/2) du

Solution: (1/2)(2/3)u^(3/2) + C = (1/3)(x² + 1)^(3/2) + C

Example 2: Trigonometric Identity

Original integral: ∫sin²x dx

Using identity: sin²x = (1 - cos(2x))/2.

Rewritten integral: (1/2)∫(1 - cos(2x)) dx

Solution: (1/2)(x - (1/2)sin(2x)) + C = (x/2) - (sin(2x)/4) + C

Frequently Asked Questions

What types of integrals can be rewritten?

This calculator can rewrite definite and indefinite integrals using substitution, integration by parts, and trigonometric identities. Complex integrals may require manual intervention.

How accurate are the solutions?

The calculator provides exact solutions when possible. For complex integrals, the solutions may be simplified forms that require further evaluation.

Can I use this calculator for homework?

Yes, this calculator can be a helpful tool for checking your work and understanding integral rewriting techniques. Always verify solutions with your instructor.