What is the integral of (2x-1)ln(x) ?

The integral of (2x-1)ln(x) is x^2ln(x)-xln(x)-(x^2)/2+x+C

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integral of (2x-1)ln(x)

\int (2 x - 1) ln (x) d x

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

Solution steps

\int (2 x - 1) ln (x) d x

Apply Integration By Parts

: ln (x) (x^{2} - x) - \int x - 1 d x

= ln (x) (x^{2} - x) - \int x - 1 d x

\int x - 1 d x = \frac{x ^{2}}{2} - x

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

Simplify

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

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

Add a constant to the solution

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

\int \frac{2 x ^{2} + x + 15}{x + 3} d x

\int_{1}^{2} 2 - x d x

y^{^{'}} = x y + 3

x \to - \infty lim (2 + e^{x})

\frac{d}{d x} (0.1 x)

What is the integral of (2x-1)ln(x) ?
The integral of (2x-1)ln(x) is x^2ln(x)-xln(x)-(x^2)/2+x+C