What is the integral from 0 to 1 of (2x-2)/(x+4) ?

The integral from 0 to 1 of (2x-2)/(x+4) is 2-10(ln(5)-2ln(2))

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integral from 0 to 1 of (2x-2)/(x+4)

\int_{0}^{1} \frac{2 x - 2}{x + 4} d x

2 - 10 (ln (5) - 2 ln (2))

Decimal

- 0.23143 \dots

Solution steps

\int_{0}^{1} \frac{2 x - 2}{x + 4} d x

Apply u-substitution

: \int_{4}^{5} \frac{2 u - 10}{u} d u

= \int_{4}^{5} \frac{2 u - 10}{u} d u

Expand

\frac{2 u - 10}{u} : 2 - \frac{10}{u}

= \int_{4}^{5} 2 - \frac{10}{u} d u

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}^{5} 2 d u - \int_{4}^{5} \frac{10}{u} d u

\int_{4}^{5} 2 d u = 2

\int_{4}^{5} \frac{10}{u} d u = 10 (ln (5) - 2 ln (2))

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

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What is the integral from 0 to 1 of (2x-2)/(x+4) ?
The integral from 0 to 1 of (2x-2)/(x+4) is 2-10(ln(5)-2ln(2))