What is the integral from-2 to 4 of (|x+1|)/(|x+6|) ?

The integral from-2 to 4 of (|x+1|)/(|x+6|) is 5ln(5)+4-15ln(2)

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integral from-2 to 4 of (|x+1|)/(|x+6|)

\int_{- 2}^{4} \frac{∣ x + 1 ∣}{∣ x + 6 ∣} d x

5 ln (5) + 4 - 15 ln (2)

Decimal Notation

1.64998 \dots

Solution steps

\int_{- 2}^{4} \frac{∣ x + 1 ∣}{∣ x + 6 ∣} d x

Eliminate Absolutes

= \int_{- 2}^{- 1} \frac{- x - 1}{x + 6} d x + \int_{- 1}^{4} \frac{x + 1}{x + 6} d x

\int_{- 2}^{- 1} \frac{- x - 1}{x + 6} d x = - 10 ln (2) + 5 ln (5) - 1

\int_{- 1}^{4} \frac{x + 1}{x + 6} d x = - 5 ln (2) + 5

= - 10 ln (2) + 5 ln (5) - 1 - 5 ln (2) + 5

Simplify

= 5 ln (5) + 4 - 15 ln (2)

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What is the integral from-2 to 4 of (|x+1|)/(|x+6|) ?
The integral from-2 to 4 of (|x+1|)/(|x+6|) is 5ln(5)+4-15ln(2)