What is the integral from 4 to 7 of 3+2ln(x+5) ?

The integral from 4 to 7 of 3+2ln(x+5) is 2ln(16777216/729)+3

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integral from 4 to 7 of 3+2ln(x+5)

\int_{4}^{7} 3 + 2 ln (x + 5) d x

2 ln (\frac{16777216}{729}) + 3

Decimal

23.08771 \dots

Solution steps

\int_{4}^{7} 3 + 2 ln (x + 5) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{4}^{7} 3 d x + \int_{4}^{7} 2 ln (x + 5) d x

\int_{4}^{7} 3 d x = 9

\int_{4}^{7} 2 ln (x + 5) d x = 2 (ln (\frac{16777216}{729}) - 3)

= 9 + 2 (ln (\frac{16777216}{729}) - 3)

Simplify

9 + 2 (ln (\frac{16777216}{729}) - 3) : 2 ln (\frac{16777216}{729}) + 3

= 2 ln (\frac{16777216}{729}) + 3

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What is the integral from 4 to 7 of 3+2ln(x+5) ?
The integral from 4 to 7 of 3+2ln(x+5) is 2ln(16777216/729)+3