What is the integral of ((log_{10}(x))*1)/x ?

The integral of ((log_{10}(x))*1)/x is log_{10}(x)ln|x|-(ln|x|^2)/(2ln(10))+C

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integral of ((log_{10}(x))*1)/x

integral

\frac{( lo g _{10} ( x ) ) \cdot 1}{x}

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

Solution steps

\int \frac{lo g _{10} ( x ) \cdot 1}{x} d x

Simplify

= \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{x}{x ^{2} - 15}

(\frac{1 + 1}{x ^{2}}) e^{\frac{x - 1}{x}}

\frac{4 x}{( x ^{3} - x ^{2} - x + 1 )}

x \cdot (x - 1)^{3}

\frac{1}{( 3 - x ) ^{\frac{3}{2}}}

What is the integral of ((log_{10}(x))*1)/x ?
The integral of ((log_{10}(x))*1)/x is log_{10}(x)ln|x|-(ln|x|^2)/(2ln(10))+C