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

The integral from-1 to 2 of x/(x+2) is 3-4ln(2)

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

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

3 - 4 ln (2)

Decimal

0.22741 \dots

Solution steps

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

Apply u-substitution

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

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

Expand

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

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

\int_{1}^{4} 1 d u = 3

\int_{1}^{4} \frac{2}{u} d u = 4 ln (2)

= 3 - 4 ln (2)

x \to 3 lim (2 x^{2} - 3 x + 4)

cot^{2} (sin (x))

\frac{d}{d x} (3 x^{3} - 5 x^{2} + 4)

x \to 2 - lim (\frac{1}{x - 3})

n = 2 \sum \infty 2 (- \frac{1}{2})^{n}

What is the integral from-1 to 2 of x/(x+2) ?
The integral from-1 to 2 of x/(x+2) is 3-4ln(2)