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Popular >

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

Popular Examples

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\int cos^{2} (θ) sin (2 θ) d θ

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\int \frac{2 x + 3}{x ^{2} + 2 x - 3} d x

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\int \frac{e ^{4 x}}{e ^{4 x} - 6} d x

integral of 2/((2x-5)ln(2x-5))

\int \frac{2}{( 2 x - 5 ) ln ( 2 x - 5 )} d x

integral of 1/(xln(x))integral

\frac{1}{x ln ( x )}

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