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

The integral of x^2log_{10}(x) is 1/3 x^3log_{10}(x)-(x^3)/(9ln(10))+C

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

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

\frac{1}{3} x^{3} lo g_{10} (x) - \frac{x ^{3}}{9 ln ( 10 )} + C

Solution steps

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

Apply Integration By Parts

: \frac{1}{3} x^{3} lo g_{10} (x) - \int \frac{x ^{2}}{3 ln ( 10 )} d x

= \frac{1}{3} x^{3} lo g_{10} (x) - \int \frac{x ^{2}}{3 ln ( 10 )} d x

\int \frac{x ^{2}}{3 ln ( 10 )} d x = \frac{x ^{3}}{9 ln ( 10 )}

= \frac{1}{3} x^{3} lo g_{10} (x) - \frac{x ^{3}}{9 ln ( 10 )}

Add a constant to the solution

= \frac{1}{3} x^{3} lo g_{10} (x) - \frac{x ^{3}}{9 ln ( 10 )} + C

f (x) = \frac{x ^{2} - 3 x + 2}{x ^{2} - 1}

y = 2.8414 x^{2} - 1.2187 x + 0.5399

\frac{d}{d x} ((x^{2} + x + 2)^{\frac{2}{3}})

y = x^{3} + 1

arcsin (\frac{x}{4})

What is the integral of x^2log_{10}(x) ?
The integral of x^2log_{10}(x) is 1/3 x^3log_{10}(x)-(x^3)/(9ln(10))+C