What is the integral of (8xln(x)) ?

The integral of (8xln(x)) is 8(1/2 x^2ln(x)-(x^2)/4)+C

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integral of (8xln(x))

\int (8 x ln (x)) d x

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

Solution steps

\int 8 x ln (x) d x

Take the constant out:

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

= 8 \cdot \int x ln (x) d x

Apply Integration By Parts

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

= 8 (\frac{1}{2} x^{2} ln (x) - \int \frac{x}{2} d x)

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

= 8 (\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4})

Add a constant to the solution

= 8 (\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}) + C

x \to \infty lim (3 x + 2)

\frac{d}{d y} (\frac{y}{2})

\int_{0}^{2} x \cdot \frac{1}{2} (2 - x) d x

\frac{d}{d x} (6 x^{3} e^{- x})

f (x) = 3 x ln (x)

What is the integral of (8xln(x)) ?
The integral of (8xln(x)) is 8(1/2 x^2ln(x)-(x^2)/4)+C