How to Integrate a Polynomial
The indefinite integral of xⁿ (n ≠ −1) is xⁿ⁺¹ / (n+1) plus a constant C.
Why + C?
Functions that differ by a constant have the same derivative, so the family of antiderivatives includes C.
Step-by-step method
- Raise each power by 1.
- Divide by the new exponent.
- Add C for an indefinite integral.
Example
∫ x² dx
- x³/3 + C
Answer: x³/3 + C
Interactive example
Solve a problem
No account required. Type, upload, or snap a photo.
Example problems
Common mistakes
Dividing by the old n
Divide by n+1, the new exponent.
Related formulas
Related calculators
Related guides
Frequently asked questions
What is a definite integral?
F(b) − F(a) for an antiderivative F, equal to net signed area under the curve.