MHB Antiderivative Question for ∫a^x dx: Is it a^x/ln a or a^x/ln|a|?

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The integral ∫a^x dx is correctly expressed as a^x/ln a when a is positive and not equal to 1. The function a^x is not defined for negative values of a, making the use of absolute values unnecessary in this context. If a is greater than zero, the absolute value notation does not apply. Therefore, the answer does not change based on the inclusion of absolute values. Understanding the conditions on a is crucial for determining the correct form of the antiderivative.
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for ∫a^x dx,

is the answer a^x/ln a or a^x/ln|a| or does it matter?

Thanks
 
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The function $a^x$ is not defined for negative values of $a$. If $a>0$ and $a\not = 1$ then what you wrote is correct without absolute values.
 
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