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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