What is the integral of (ln(x)+x) ?

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

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integral of (ln(x)+x)

\int (ln (x) + x) d x

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

Solution steps

\int 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 ln (x) d x + \int x d x

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

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

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

Add a constant to the solution

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

\frac{1}{( ( 25 s ^{2} + 19980 ) )}

\frac{\partial}{\partial x} (\frac{1}{x} sin (\frac{y}{x}))

\int (x - 1) sin (π) x d x

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\int \frac{1}{3 x + 1} d x

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