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

Popular >

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

\frac{\partial}{\partial t} (\frac{c}{x + c t})

x \to - 5 lim (\frac{x ^{2} - 4}{5 - x})

\int \frac{x ^{2}}{( x ^{2} - 36 ) ^{\frac{5}{2}}} d x

\int \frac{tan ^{3} ( \frac{6}{z} )}{z ^{2}} d z

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