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

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

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integral of x*log_{10}(x)

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

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

Solution steps

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

Apply Integration By Parts

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

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

\int \frac{x}{2 ln ( 10 )} d x = \frac{x ^{2}}{4 ln ( 10 )}

= \frac{1}{2} x^{2} lo g_{10} (x) - \frac{x ^{2}}{4 ln ( 10 )}

Add a constant to the solution

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

m \to 4 lim (\frac{3 m ^{2} - 8 m - 16}{2 m ^{2} - 9 m + 4})

\int 8 y - 24 d y

x \to 5 + lim (\frac{- 1}{x ^{2} - 25})

\int 9 θ cos (θ) d θ

x^{2} - 3, 2 x

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