What does this integral calculator do?
It finds the antiderivative of a·xⁿ with the power rule and can evaluate a definite integral from A to B.
Integral Calculator
Integrate a·xⁿ with the power rule, and optionally evaluate a definite integral from A to B.
Enter the integrand
Provide coefficient a and exponent n. Leave A and B blank for an indefinite integral.
About this calculator
How to use Integral Calculator, plus the formulas and logic behind the results.
Tool description
This educational tool applies the power rule for ∫ a xⁿ dx. When n = −1 the antiderivative is a ln|x|. Definite integrals evaluate F(B) − F(A).
How to use
- Enter the coefficient a and the power n of x.
- Optionally enter lower limit A and upper limit B for a definite integral.
- Select Calculate to view the antiderivative and value.
- Adjust a, n, or limits and recalculate as needed.
Formulas & reference
∫ a xⁿ dx = a xⁿ⁺¹ / (n+1) + C (n ≠ −1)∫ a x⁻¹ dx = a ln|x| + C∫_A^B f(x) dx = F(B) − F(A)
Integral tips
- Power rule fails at n = −1; use the natural log form
- Definite integrals need both A and B
- Constants of integration appear only for indefinite integrals
- Check that F is continuous on [A, B]
Calculation logic
Applies the power rule (or log rule when n = −1). If both limits are provided, evaluates the definite integral numerically from the antiderivative.
Educational calculator for monomials only—not a full computer algebra system.
Integral Calculator FAQ
Common questions about this calculator and how to use the results.
What if n equals −1?
The antiderivative becomes a ln|x| + C instead of a power of x.
Do I need limits A and B?
No. Leave them blank for an indefinite integral with + C.
Can I integrate polynomials?
Enter each power term separately, or use the area-under-the-curve tool for ax²+bx+c.
Is the answer exact?
Symbolic forms are shown when simple; numeric definite results are rounded for display.
Is this free?
Yes. LeCalculators calculus tools are free to use in your browser.