The Indefinite Integral Calculator finds an antiderivative of a function. Instead of evaluating between two endpoints, it returns a function whose derivative reproduces the original integrand.
What an Indefinite Integral Means
The basic relationship is ∫f(x)dx = F(x) + C, where F′(x)=f(x). The constant C is included because every constant disappears when differentiated, so there are infinitely many antiderivatives that differ only by a constant.
Using the Calculator
Enter the integrand and use the notation supported by the tool. Review powers, fractions, roots, and trigonometric functions carefully. The result should be checked by differentiating it back to the original expression.
Example
For ∫3x² dx, increase the power from 2 to 3 and divide by the new power: x³ + C. Differentiating x³ + C gives 3x², confirming the result.
Why the Constant Matters
Leaving out C gives one antiderivative but not the complete family. A definite integral does not need this arbitrary constant because it cancels when endpoint values are subtracted.
When to Use It
Indefinite integration is useful for reversing differentiation, constructing general solution forms, and preparing expressions for definite integration. For more complicated functions, the calculator can save time while still allowing you to verify the answer by differentiation.