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Integrals · Basic Antiderivatives

Power Rule for Integration

∫xn dx=xn+1n+1+C(n≠−1)\int x^n \, dx = \frac{x^{n+1}}{n+1} + C \quad (n \neq -1)

The reverse of the power rule for derivatives. Increase the exponent by 1 and divide by the new exponent.

Conditions. n ≠ -1 (that case gives ln|x|).
  • 3 worked examples
  • 19 in Integrals

Worked examples

Find ∫ x⁴ dx.
  1. x⁵/5 + C

Answer: x⁵/5 + C

2 more worked examplesPremium

Find ∫ 1/x³ dx.

Step-by-step solution locked.

Find ∫ √x dx.

Step-by-step solution locked.

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Common questions

What is the Power Rule for Integration?

The reverse of the power rule for derivatives. Increase the exponent by 1 and divide by the new exponent. It is one of the integrals formulas in the CalcRef reference.

When does the Power Rule for Integration apply?

The Power Rule for Integration holds under this condition: n ≠ -1 (that case gives ln|x|).

How do you use the Power Rule for Integration?

Worked example. Find ∫ x⁴ dx. x⁵/5 + C. Answer: x⁵/5 + C.

Practice

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