What is the integral of log_{a}(x) ?

The integral of log_{a}(x) is xlog_{a}(x)-x/(ln(a))+C

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integral of log_{a}(x)

\int lo g_{a} (x) d x

x lo g_{a} (x) - \frac{x}{ln ( a )} + C

Solution steps

\int lo g_{a} (x) d x

Apply Integration By Parts

: x lo g_{a} (x) - \int \frac{1}{ln ( a )} d x

= x lo g_{a} (x) - \int \frac{1}{ln ( a )} d x

\int \frac{1}{ln ( a )} d x = \frac{x}{ln ( a )}

= x lo g_{a} (x) - \frac{x}{ln ( a )}

Add a constant to the solution

= x lo g_{a} (x) - \frac{x}{ln ( a )} + C

\frac{\partial}{\partial y} (x y^{\frac{1}{2}})

\frac{d}{d x} ((3 - x^{2}) (x^{3} - 5 x + 2))

\frac{d x}{d t} = t x - 2 x + t - 2

\int \frac{x}{4 + 9 x ^{2}} d x

x \to 0 lim (\frac{1 - cot ( x )}{\frac{1}{x}})

What is the integral of log_{a}(x) ?
The integral of log_{a}(x) is xlog_{a}(x)-x/(ln(a))+C