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Popular >

integral of x-ln(x)

Solution

\int x - ln (x) d x

Solution

\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

Graph

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\frac{d}{d x} ((3 x)^{5 x})

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\int a x + b d x

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Frequently Asked Questions (FAQ)

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