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Integrals · Basic Antiderivatives

Integral of aˣ

∫ax dx=axln⁡a+C\int a^x \, dx = \frac{a^x}{\ln a} + C

The antiderivative of a general exponential function.

Conditions. a > 0, a ≠ 1.
  • 2 worked examples
  • 19 in Integrals

Worked examples

Find ∫ 2ˣ dx.
  1. 2ˣ / ln 2 + C

Answer: 2ˣ / ln 2 + C

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Evaluate ∫₀¹ 3ˣ dx.

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Common questions

What is the Integral of aˣ?

The antiderivative of a general exponential function. It is one of the integrals formulas in the CalcRef reference.

When does the Integral of aˣ apply?

The Integral of aˣ holds under this condition: a > 0, a ≠ 1.

How do you use the Integral of aˣ?

Worked example. Find ∫ 2ˣ dx. 2ˣ / ln 2 + C. Answer: 2ˣ / ln 2 + C.

Practice

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