What is the integral from 1 to 2 of xln(8x) ?

The integral from 1 to 2 of xln(8x) is -3/4+13/2 ln(2)

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integral from 1 to 2 of xln(8x)

\int_{1}^{2} x ln (8 x) d x

- \frac{3}{4} + \frac{13}{2} ln (2)

Decimal Notation

3.75545 \dots

Solution steps

\int_{1}^{2} x ln (8 x) d x

Apply Integration By Parts

: [\frac{1}{2} x^{2} ln (8 x) - \int \frac{x}{2} d x]_{1}^{2}

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

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

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

Compute the boundaries:

- \frac{3}{4} + \frac{13}{2} ln (2)

= - \frac{3}{4} + \frac{13}{2} ln (2)

\int \frac{x ^{2} + 1}{( x - 5 ) ( x - 4 ) ^{2}} d x

\frac{d}{d t} (a t cos (4 t) + b t sin (4 t))

\frac{\partial}{\partial x} (- x^{2} sin (x^{2} y))

n \to \infty lim (\frac{4}{n})

\frac{d}{d x} ((2 x + e^{x}) (5 - x))

What is the integral from 1 to 2 of xln(8x) ?
The integral from 1 to 2 of xln(8x) is -3/4+13/2 ln(2)