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

Lösung

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

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

Dezimale

2.88629 \dots

Schritte zur Lösung

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

Multipliziere aus

(\frac{x + 1}{x})^{2} : 1 + \frac{2}{x} + \frac{1}{x ^{2}}

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

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int_{1}^{2} 1 d x = 1

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

\int_{1}^{2} \frac{1}{x ^{2}} d x = \frac{1}{2}

= 1 + 2 ln (2) + \frac{1}{2}

Ziehe Brüche zusammen

1 + \frac{1}{2} : \frac{3}{2}

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

\int_{- 3}^{2} (- 2 x) d x

\int_{0}^{1} 15 x e^{x} d x

\int_{0}^{1} x \cdot 2 (1 - x) d x

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

\int_{- 2}^{2} - (1 - x^{2}) d x