What is the integral of-2xln(x) ?

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

integral of-2xln(x)

\int - 2 x ln (x) d x

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

Solution steps

\int - 2 x ln (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - 2 \cdot \int x ln (x) d x

Apply Integration By Parts

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

\int \frac{x}{2} d x = \frac{x ^{2}}{4}

= - 2 (\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4})

Simplify

- 2 (\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}) : - x^{2} ln (x) + \frac{x ^{2}}{2}

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

Add a constant to the solution

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

\int - 2 x^{3} d x

\frac{\partial}{\partial x} (\frac{x ^{2}}{2} + \frac{y ^{3}}{3})

d er i v a t i v e f (x) = 5 e x

\frac{d}{d t} (t^{\frac{1}{2}})

x \to 0 lim (\frac{( 3 + x ^{2} ) - 9}{x})

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