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Popular Calculus >

integral of ln(x)+x

Solution

\int ln (x) + x d x

Solution

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

Graph

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Frequently Asked Questions (FAQ)

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