integral from 1 to 5 of (1+1/x+1/(x^2))

Lösung

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

ln (5) + \frac{24}{5}

Dezimale

6.40943 \dots

Schritte zur Lösung

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

\int_{1}^{5} 1 d x = 4

\int_{1}^{5} \frac{1}{x} d x = ln (5)

\int_{1}^{5} \frac{1}{x ^{2}} d x = \frac{4}{5}

= 4 + ln (5) + \frac{4}{5}

Ziehe Brüche zusammen

4 + \frac{4}{5} : \frac{24}{5}

= ln (5) + \frac{24}{5}

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

\int_{0}^{1} (4 t - 1)^{2} d t

\int_{0}^{4} π (x + 3)^{2} d x

\int_{2}^{3} x^{2} + 2 x + 2 - 5 d x

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