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

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

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

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

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

Solution steps

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

Simplify

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

Apply Integration By Parts

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

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

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

= x lo g_{10} (x)^{2} - \frac{2}{ln ^{2} ( 10 )} (x ln (x) - x)

Add a constant to the solution

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

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