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

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

\frac{d y}{d x} = e^{- 2 x}

\frac{d y}{d x} = 3 y - x^{2} y

\frac{d}{d x} (tan (1))

x \to 1 lim (\frac{4}{x ^{3} - 1})

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