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Home › TS EAPCET (Engineering) › Mathematics › Integration by Substitution › What is ∫ aˣ dx for a constant a > 0, a ≠ 1?

What is ∫ aˣ dx for a constant a > 0, a ≠ 1?

Aaˣ + C
Baˣ/ln a + C
Cx aˣ⁻¹ + C
Daˣ ln a + C
Answer & Solution
Correct answer: B. aˣ/ln a + C
Since d/dx(aˣ) = aˣ ln a, dividing by ln a gives the antiderivative aˣ/ln a.
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