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

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

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integral of (x-ln(x))

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

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

Solution steps

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

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

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

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

Simplify

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

Add a constant to the solution

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

\frac{s + 2}{s ^{2} + 4 s + 13}

\int 5 sin^{5} (x) cos^{- \frac{3}{2}} (x) d x

\int cos^{3} (6 x) sin^{- 2} (6 x) d x

- x^{3} - 5 x^{2} + 3 x - 1

x \to 4 + lim (\frac{∣ 4 - x ∣}{4 - x})

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