What is the integral of log_{10}(3x-2) ?

The integral of log_{10}(3x-2) is xlog_{10}(3x-2)-(3x-2+2ln|3x-2|)/(3ln(10))+C

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integral of log_{10}(3x-2)

integral

lo g_{10} (3 x - 2)

x lo g_{10} (3 x - 2) - \frac{3 x - 2 + 2 ln ∣ 3 x - 2 ∣}{3 ln ( 10 )} + C

Solution steps

\int lo g_{10} (3 x - 2) d x

Apply Integration By Parts

= x lo g_{10} (3 x - 2) - \int \frac{3 x}{ln ( 10 ) ( 3 x - 2 )} d x

\int \frac{3 x}{ln ( 10 ) ( 3 x - 2 )} d x = \frac{3 x - 2 + 2 ln ∣ 3 x - 2 ∣}{3 ln ( 10 )}

= x lo g_{10} (3 x - 2) - \frac{3 x - 2 + 2 ln ∣ 3 x - 2 ∣}{3 ln ( 10 )}

Add a constant to the solution

= x lo g_{10} (3 x - 2) - \frac{3 x - 2 + 2 ln ∣ 3 x - 2 ∣}{3 ln ( 10 )} + C

What is the integral of log_{10}(3x-2) ?
The integral of log_{10}(3x-2) is xlog_{10}(3x-2)-(3x-2+2ln|3x-2|)/(3ln(10))+C