What is the integral of xln(x)-x ?

The integral of xln(x)-x is 1/2 x^2ln(x)-(x^2)/4-(x^2)/2+C

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integral of xln(x)-x

\int x ln (x) - x d x

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

Solution steps

\int x ln (x) - x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x ln (x) d x - \int x d x

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

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

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

Add a constant to the solution

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

\int \frac{1}{2 x ^{2} - 5 x + 3} d x

\int_{0}^{1} x^{\frac{1}{3}} - x^{3} d x

\int x 9 36 + x^{2} d x

\int cos (3 x) cos (2 x) cos (x) d x

y^{^{'}} = \frac{( 6 x ^{4} e ^{\frac{y}{x}} + x ^{2} y ^{2} )}{x ^{3} y}

What is the integral of xln(x)-x ?
The integral of xln(x)-x is 1/2 x^2ln(x)-(x^2)/4-(x^2)/2+C