What is the integral of (log_{4}(x))/x ?

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

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integral of (log_{4}(x))/x

\int \frac{lo g _{4} ( x )}{x} d x

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

Solution steps

\int \frac{lo g _{4} ( x )}{x} d x

Apply Integration By Parts

= lo g_{4} (x) ln ∣ x ∣ - \int \frac{ln ∣ x ∣}{2 ln ( 2 ) x} d x

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

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

Add a constant to the solution

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

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