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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

Add a constant to the solution

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

Popular Examples

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x \to - 4 lim (5 x - 6)

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integral of sqrt(x)-(x-2)

\int x - (x - 2) d x

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