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

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

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

Simplify

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

\int_{0}^{1} x ln (x^{2} + 1) d x

\int_{0}^{1} \frac{1}{2} cosh (2 x) d x

\int_{1}^{3} \frac{2}{x ^{2} + 1} d x

\int_{- 1}^{1} \frac{x + 5}{x ^{2} + 2 x + 5} d x

\int_{0}^{4} \frac{1}{x ^{3}} d x

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)