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

The integral of xlog_{x}(x) is (x^2)/2+C

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integral of xlog_{x}(x)

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

\frac{x ^{2}}{2} + C

Solution steps

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

Simplify

x lo g_{x} (x) : x

= \int x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

= \frac{x ^{2}}{2}

Add a constant to the solution

= \frac{x ^{2}}{2} + C

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