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

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

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integral of x*log_{e}(x)

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

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

Solution steps

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

Apply Integration By Parts

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

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

\int \frac{x}{2} d x = \frac{x ^{2}}{4}

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

Add a constant to the solution

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

\int_{9}^{24} (- x + 12) d x

ln (s)

y^{^{'}} = \frac{3 y ^{2} + 4 x}{2 x y}

\int \frac{x ^{2}}{- 4 x ^{2} - 12 x - 5} d x

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