Finding the Antiderivative of a^x Using the Power Rule for Antiderivatives and Simplifying

antiderivative of a^x

The antiderivative of a^x, where “a” is a constant, can be found using the power rule for antiderivatives

The antiderivative of a^x, where “a” is a constant, can be found using the power rule for antiderivatives.

The power rule states that the antiderivative of x^n is (1/(n+1)) * x^(n+1), where n is a constant and not equal to -1.

Applying this rule to a^x, we can write it as (a^x)/(ln(a)) * ln(a). The derivative of ln(a) is simply 1. So the antiderivative of a^x is given by:

∫ a^x dx = (1/ln(a)) * (a^x)

In other words, the antiderivative of a^x is (a^x)/(ln(a)) times a constant, which is (1/ln(a)).

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