What is the integral of (log_{9}(x))/x ?

The integral of (log_{9}(x))/x is log_{9}(x)ln|x|-(ln|x|^2)/(4ln(3))+C

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integral of (log_{9}(x))/x

\int \frac{lo g _{9} ( x )}{x} d x

lo g_{9} (x) ln ∣ x ∣ - \frac{ln ∣ x ∣ ^{2}}{4 ln ( 3 )} + C

Solution steps

\int \frac{lo g _{9} ( x )}{x} d x

Apply Integration By Parts

: lo g_{9} (x) ln ∣ x ∣ - \int \frac{ln ∣ x ∣}{2 ln ( 3 ) x} d x

= lo g_{9} (x) ln ∣ x ∣ - \int \frac{ln ∣ x ∣}{2 ln ( 3 ) x} d x

\int \frac{ln ∣ x ∣}{2 ln ( 3 ) x} d x = \frac{ln ∣ x ∣ ^{2}}{4 ln ( 3 )}

= lo g_{9} (x) ln ∣ x ∣ - \frac{ln ∣ x ∣ ^{2}}{4 ln ( 3 )}

Add a constant to the solution

= lo g_{9} (x) ln ∣ x ∣ - \frac{ln ∣ x ∣ ^{2}}{4 ln ( 3 )} + C

f (x) = \frac{3 x + 2}{x - 1}

\frac{\partial}{\partial x} (81 x^{8} y^{8} - 64 x^{7} y^{7})

\int_{0}^{\frac{π}{2}} x cos (x^{2}) d x

(5 - 5 x^{3})^{3} + \frac{1}{5 - 5 x ^{3}}

\int xx d x

What is the integral of (log_{9}(x))/x ?
The integral of (log_{9}(x))/x is log_{9}(x)ln|x|-(ln|x|^2)/(4ln(3))+C