What is the integral from 1 to 2 of xln(4x) ?

The integral from 1 to 2 of xln(4x) is 5ln(2)-3/4

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integral from 1 to 2 of xln(4x)

\int_{1}^{2} x ln (4 x) d x

5 ln (2) - \frac{3}{4}

Decimal

2.71573 \dots

Solution steps

\int_{1}^{2} x ln (4 x) d x

Apply Integration By Parts

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

Compute the boundaries:

5 ln (2) - \frac{3}{4}

= 5 ln (2) - \frac{3}{4}

What is the integral from 1 to 2 of xln(4x) ?
The integral from 1 to 2 of xln(4x) is 5ln(2)-3/4