How to use this calculator
Choose an indefinite integral to find an antiderivative, or a definite integral to evaluate it between two bounds. Enter one constant or one power of a single-letter variable, such as 5, x^2 or 3*x^2.
Method and interpretation
For a*x^n with n not equal to -1, the antiderivative is a*x^(n+1)/(n+1) + C. For x^-1 it is ln|x| + C. A definite integral evaluates F(upper) - F(lower); reversing the bounds changes its sign.
Assumptions and limits
This tool supports constants and single powers, not arbitrary sums, trigonometric functions or general symbolic expressions. It rejects intervals crossing a zero singularity and negative bounds for fractional powers. A negative result is signed accumulation, not necessarily geometric area.
Definite and indefinite integrals: which should I choose?
Choose Indefinite when you need a family of antiderivatives, including the integration constant C. Choose Definite when you have lower and upper bounds and need a numerical value. For example, x^2 has antiderivative x^3/3 + C, while its definite integral from 0 to 3 is 9.
This power-rule calculator supports one constant or one power term. It is not a general symbolic integration solver: expressions such as x^2 + x, sin(x), and integration by parts require a different method.
How do I enter a power function?
Use ^ for exponents and * for multiplication: enter 3*x^2 for three times x squared, or x^-1 for the reciprocal of x. Use x as the integration variable shown beside the expression field. For a definite integral, enter both bounds before calculating.
An integral can be negative. Integrating a negative function over increasing bounds gives negative signed accumulation, and reversing the bounds reverses the sign. Geometric area requires additional treatment when a function crosses the axis.
Worked example
For 3*x^2, an antiderivative is x^3 + C. From 0 to 2, the definite integral is 2^3 - 0^3 = 8. The constant C cancels when subtracting the endpoint values.