What is the integral from 1 to 2 of (3x+2)ln(x) ?

The integral from 1 to 2 of (3x+2)ln(x) is 10ln(2)-17/4

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integral from 1 to 2 of (3x+2)ln(x)

\int_{1}^{2} (3 x + 2) ln (x) d x

10 ln (2) - \frac{17}{4}

Decimal Notation

2.68147 \dots

Solution steps

\int_{1}^{2} (3 x + 2) ln (x) d x

Apply Integration By Parts

: [ln (x) (\frac{3 x ^{2}}{2} + 2 x) - \int \frac{1}{2} (3 x + 4) d x]_{1}^{2}

= [ln (x) (\frac{3 x ^{2}}{2} + 2 x) - \int \frac{1}{2} (3 x + 4) d x]_{1}^{2}

\int \frac{1}{2} (3 x + 4) d x = \frac{1}{2} (\frac{3 x ^{2}}{2} + 4 x)

= [ln (x) (\frac{3 x ^{2}}{2} + 2 x) - \frac{1}{2} (\frac{3 x ^{2}}{2} + 4 x)]_{1}^{2}

Compute the boundaries:

10 ln (2) - \frac{17}{4}

= 10 ln (2) - \frac{17}{4}

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What is the integral from 1 to 2 of (3x+2)ln(x) ?
The integral from 1 to 2 of (3x+2)ln(x) is 10ln(2)-17/4