What is the integral of (log_{7}(x))/x ?

The integral of (log_{7}(x))/x is log_{7}(x)ln|x|-(ln|x|^2)/(2ln(7))+C

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integral of (log_{7}(x))/x

\int \frac{lo g _{7} ( x )}{x} d x

lo g_{7} (x) ln ∣ x ∣ - \frac{ln ∣ x ∣ ^{2}}{2 ln ( 7 )} + C

Solution steps

\int \frac{lo g _{7} ( x )}{x} d x

Apply Integration By Parts

: lo g_{7} (x) ln ∣ x ∣ - \int \frac{ln ∣ x ∣}{ln ( 7 ) x} d x

= lo g_{7} (x) ln ∣ x ∣ - \int \frac{ln ∣ x ∣}{ln ( 7 ) x} d x

\int \frac{ln ∣ x ∣}{ln ( 7 ) x} d x = \frac{ln ∣ x ∣ ^{2}}{2 ln ( 7 )}

= lo g_{7} (x) ln ∣ x ∣ - \frac{ln ∣ x ∣ ^{2}}{2 ln ( 7 )}

Add a constant to the solution

= lo g_{7} (x) ln ∣ x ∣ - \frac{ln ∣ x ∣ ^{2}}{2 ln ( 7 )} + C

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What is the integral of (log_{7}(x))/x ?
The integral of (log_{7}(x))/x is log_{7}(x)ln|x|-(ln|x|^2)/(2ln(7))+C