What is the integral of (log_{10}(x))/(x^3) ?

The integral of (log_{10}(x))/(x^3) is (log_{10}(x))/(x^2)-(6ln(x)+1)/(4ln(10)x^2)+C

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integral of (log_{10}(x))/(x^3)

\int \frac{lo g _{10} ( x )}{x ^{3}} d x

\frac{lo g _{10} ( x )}{x ^{2}} - \frac{6 ln ( x ) + 1}{4 ln ( 10 ) x ^{2}} + C

Solution steps

\int \frac{lo g _{10} ( x )}{x ^{3}} d x

Apply Integration By Parts

: \frac{lo g _{10} ( x )}{x ^{2}} - \int \frac{1 - 3 ln ( x )}{ln ( 10 ) x ^{3}} d x

= \frac{lo g _{10} ( x )}{x ^{2}} - \int \frac{1 - 3 ln ( x )}{ln ( 10 ) x ^{3}} d x

\int \frac{1 - 3 ln ( x )}{ln ( 10 ) x ^{3}} d x = \frac{6 ln ( x ) + 1}{4 ln ( 10 ) x ^{2}}

= \frac{lo g _{10} ( x )}{x ^{2}} - \frac{6 ln ( x ) + 1}{4 ln ( 10 ) x ^{2}}

Add a constant to the solution

= \frac{lo g _{10} ( x )}{x ^{2}} - \frac{6 ln ( x ) + 1}{4 ln ( 10 ) x ^{2}} + C

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What is the integral of (log_{10}(x))/(x^3) ?
The integral of (log_{10}(x))/(x^3) is (log_{10}(x))/(x^2)-(6ln(x)+1)/(4ln(10)x^2)+C