What is the integral of-4xln(x) ?

The integral of-4xln(x) is -2x^2ln(x)+x^2+C

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integral of-4xln(x)

\int - 4 x ln (x) d x

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

Solution steps

\int - 4 x ln (x) d x

Take the constant out:

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

= - 4 \cdot \int x ln (x) d x

Apply Integration By Parts

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

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

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

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

Simplify

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

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

Add a constant to the solution

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

(ln (x))^{2}

\frac{d}{d x} (\frac{- x sin ( x ) - cos ( x )}{x ^{2}})

\int_{1}^{2} x \cdot ln (x) d x

n = 0 \sum \infty \frac{1}{( n ^{2} + 1 )}

y = \frac{2}{x - 6}, (8, 1)