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

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

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integral of log_{10}(ax)

\int lo g_{10} (a x) d x

x lo g_{10} (a x) - \frac{1}{ln ( 10 )} x + C

Solution steps

\int lo g_{10} (a x) d x

Apply Integration By Parts

: x lo g_{10} (a x) - \int \frac{1}{ln ( 10 )} d x

= x lo g_{10} (a x) - \int \frac{1}{ln ( 10 )} d x

\int \frac{1}{ln ( 10 )} d x = \frac{1}{ln ( 10 )} x

= x lo g_{10} (a x) - \frac{1}{ln ( 10 )} x

Add a constant to the solution

= x lo g_{10} (a x) - \frac{1}{ln ( 10 )} x + C

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