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

The integral from 2 to 4 of x/(x+2) is 2-2ln(3/2)

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integral from 2 to 4 of x/(x+2)

\int_{2}^{4} \frac{x}{x + 2} d x

2 - 2 ln (\frac{3}{2})

Solution steps

\int_{2}^{4} \frac{x}{x + 2} d x

Apply u-substitution

: \int_{4}^{6} \frac{u - 2}{u} d u

= \int_{4}^{6} \frac{u - 2}{u} d u

Expand

\frac{u - 2}{u} : 1 - \frac{2}{u}

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

\int_{4}^{6} 1 d u = 2

\int_{4}^{6} \frac{2}{u} d u = 2 ln (\frac{3}{2})

= 2 - 2 ln (\frac{3}{2})

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What is the integral from 2 to 4 of x/(x+2) ?
The integral from 2 to 4 of x/(x+2) is 2-2ln(3/2)