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

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

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integral of log_{10}(x+2)

integral

lo g_{10} (x + 2)

x lo g_{10} (x + 2) - \frac{1}{ln ( 10 )} (x + 2 - 2 ln ∣ x + 2 ∣) + C

Solution steps

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

Apply Integration By Parts

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

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

= x lo g_{10} (x + 2) - \frac{1}{ln ( 10 )} (x + 2 - 2 ln ∣ x + 2 ∣)

Add a constant to the solution

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

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