What is the integral of (log_{10}(x))/x ?

The integral of (log_{10}(x))/x is log_{10}(x)ln|x|-(ln|x|^2)/(2ln(10))+C

Popular >

integral of (log_{10}(x))/x

\int \frac{lo g _{10} ( x )}{x} d x

lo g_{10} (x) ln ∣ x ∣ - \frac{ln ∣ x ∣ ^{2}}{2 ln ( 10 )} + C

Solution steps

\int \frac{lo g _{10} ( x )}{x} d x

Apply Integration By Parts

: lo g_{10} (x) ln ∣ x ∣ - \int \frac{ln ∣ x ∣}{ln ( 10 ) x} d x

= lo g_{10} (x) ln ∣ x ∣ - \int \frac{ln ∣ x ∣}{ln ( 10 ) x} d x

\int \frac{ln ∣ x ∣}{ln ( 10 ) x} d x = \frac{ln ∣ x ∣ ^{2}}{2 ln ( 10 )}

= lo g_{10} (x) ln ∣ x ∣ - \frac{ln ∣ x ∣ ^{2}}{2 ln ( 10 )}

Add a constant to the solution

= lo g_{10} (x) ln ∣ x ∣ - \frac{ln ∣ x ∣ ^{2}}{2 ln ( 10 )} + C

\frac{d}{d t} (e^{t^{2} - t})

arctan (\frac{x}{2})

2 y^{^{''}} + 50 y = 0

\int 1 - \frac{2 x}{x ^{2} + 1} d x

\int \frac{x ^{3} - 2 x ^{4} + x ^{5}}{2} d x

What is the integral of (log_{10}(x))/x ?
The integral of (log_{10}(x))/x is log_{10}(x)ln|x|-(ln|x|^2)/(2ln(10))+C