LaTeX
\int x^n\,dx=\frac{x^{n+1}}{n+1}+CVariables
- n: exponent not equal to −1
- C: integration constant
How to use this formula
Integrates a power of x when n is not −1.
Important notes
- The case n=−1 gives ln|x|+C.
Quick example
∫x²dx=x³/3+C.
Applicability, worked calculation, and verification
Assumptions and domain checks
- The case n=−1 gives ln|x|+C.
- For the Integral Power Rule, every denominator must be nonzero, and the numerator and denominator must remain correctly grouped.
- Integration limits, the differential, and any constant of integration must be included where required.
- The function must satisfy the differentiability, continuity, or integrability conditions required by the operation being used.
Worked example
∫x²dx=x³/3+C.
Common mistakes
- When copying Integral Power Rule, keep the complete numerator and denominator grouped; a missing brace or parenthesis changes the result.
- Do not apply a differentiation or integration rule outside its domain or omit endpoint, continuity, or constant-of-integration checks.
Continue the workflow
Use Integral Power Rule in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
\int x^n\,dx=\frac{x^{n+1}}{n+1}+C. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Calculus Volume 1OpenStax, Rice University — Reviewed limits, derivatives, integrals, and foundational calculus formulas.
Frequently asked questions
What is the Integral Power Rule used for?
Integrates a power of x when n is not −1.
Can I copy this formula as LaTeX?
Yes. Copy \int x^n\,dx=\frac{x^{n+1}}{n+1}+C or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.