What is the integral from 3 to 6 of (x+1)ln(2x+4) ?

The integral from 3 to 6 of (x+1)ln(2x+4) is 96ln(2)-27/4-15/2 ln(10)

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integral from 3 to 6 of (x+1)ln(2x+4)

\int_{3}^{6} (x + 1) ln (2 x + 4) d x

96 ln (2) - \frac{27}{4} - \frac{15}{2} ln (10)

Decimal

42.52274 \dots

Solution steps

\int_{3}^{6} (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]_{3}^{6}

= [ln (2 x + 4) (\frac{x ^{2}}{2} + x) - \int \frac{x}{2} d x]_{3}^{6}

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

= [ln (2 x + 4) (\frac{x ^{2}}{2} + x) - \frac{x ^{2}}{4}]_{3}^{6}

Compute the boundaries:

96 ln (2) - \frac{27}{4} - \frac{15}{2} ln (10)

= 96 ln (2) - \frac{27}{4} - \frac{15}{2} ln (10)

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What is the integral from 3 to 6 of (x+1)ln(2x+4) ?
The integral from 3 to 6 of (x+1)ln(2x+4) is 96ln(2)-27/4-15/2 ln(10)