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

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

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integral of xlog_{10}(x)

\int x 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

x \to \frac{π}{4} lim (sin (x))

f (x) = \frac{x}{3 x + 4 ln ( x )}

\frac{d y}{d x}, y^{2} = 4 x

\frac{\partial}{\partial y} (x y - y^{2})

\frac{d ^{2}}{d x ^{2}} (\frac{x ^{2}}{7 + 6 x})

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