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

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SUMMARY

The integral of the function ∫a^x dx is definitively a^x/ln a when a is greater than 0 and not equal to 1. The use of absolute values, as in a^x/ln|a|, is unnecessary in this case since the function a^x is not defined for negative values of a. Therefore, for positive values of a, the expression a^x/ln a is the correct formulation for 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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