What is the integral from 5 to 8 of (x+1)ln(2x+4) ?

The integral from 5 to 8 of (x+1)ln(2x+4) is 40ln(20)-39/4-35/2 ln(14)

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integral from 5 to 8 of (x+1)ln(2x+4)

\int_{5}^{8} (x + 1) ln (2 x + 4) d x

40 ln (20) - \frac{39}{4} - \frac{35}{2} ln (14)

Decimal

63.89578 \dots

Solution steps

\int_{5}^{8} (x + 1) ln (2 x + 4) d x

Apply Integration By Parts

= [ln (2 x + 4) (\frac{x ^{2}}{2} + x) - \int \frac{x}{2} d x]_{5}^{8}

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

= [ln (2 x + 4) (\frac{x ^{2}}{2} + x) - \frac{x ^{2}}{4}]_{5}^{8}

Compute the boundaries:

40 ln (20) - \frac{39}{4} - \frac{35}{2} ln (14)

= 40 ln (20) - \frac{39}{4} - \frac{35}{2} ln (14)

What is the integral from 5 to 8 of (x+1)ln(2x+4) ?
The integral from 5 to 8 of (x+1)ln(2x+4) is 40ln(20)-39/4-35/2 ln(14)