Integral of a Logarithm with Arbitrary Base

Rarely Tested

Integral of a Logarithm with Arbitrary Base

For $$a>0$$ and $$a\neq1$$:

$$\int\log_a x\,dx=\frac{x\ln x-x}{\ln a}+C$$

Usage

- Used when logarithms have a base other than $$e$$.

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