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

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

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integral of xlog_{e}(x)

\int x 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

x \to 0 lim (sin^{x} (x))

\frac{d}{d x} (cos (x^{2} - 2 x))

y = \frac{2}{e ^{x} + e ^{- x}}

\int z cos (z) d z

9 y^{^{''}} + 10 y = 0, y (π) = 1

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