CalcRef

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.

Worked examples

Find ∫ 2ˣ dx.
  1. 2ˣ / ln 2 + C

Answer: 2ˣ / ln 2 + C

Evaluate ∫₀¹ 3ˣ dx.
  1. [3ˣ/ln 3]₀¹ = (3 - 1)/ln 3 = 2/ln 3

Answer: 2/ln 3 ≈ 1.820

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