What is the integral of 1/(x^2)log_{10}(x) ?

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

integral of 1/(x^2)log_{10}(x)

integral

\frac{1}{x ^{2}} lo g_{10} (x)

\frac{lo g _{10} ( x )}{x} - \frac{2 ln ( x ) + 1}{ln ( 10 ) x} + C

Solution steps

\int \frac{1}{x ^{2}} lo g_{10} (x) d x

Simplify

\frac{1}{x ^{2}} lo g_{10} (x) : \frac{lo g _{10} ( x )}{x ^{2}}

= \int \frac{lo g _{10} ( x )}{x ^{2}} d x

Apply Integration By Parts

= \frac{lo g _{10} ( x )}{x} - \int \frac{1 - 2 ln ( x )}{ln ( 10 ) x ^{2}} d x

\int \frac{1 - 2 ln ( x )}{ln ( 10 ) x ^{2}} d x = \frac{2 ln ( x ) + 1}{ln ( 10 ) x}

= \frac{lo g _{10} ( x )}{x} - \frac{2 ln ( x ) + 1}{ln ( 10 ) x}

Add a constant to the solution

= \frac{lo g _{10} ( x )}{x} - \frac{2 ln ( x ) + 1}{ln ( 10 ) x} + C

in t e g r a l 2 t + 3

in t e g r a l \frac{( x ^{2} + 1 ) e ^{x}}{( x + 1 ) ^{2}}

in t e g r a l e^{6 x}

in t e g r a l \frac{sin ^{2} ( x ) tan ^{2} ( x )}{2}

in t e g r a l \frac{x}{x - 1}

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