integral from 2 to 5 of (3x+3)/(x^2)

Lösung

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

3 (ln (5) - ln (2)) + \frac{9}{10}

Dezimale

3.64887 \dots

Schritte zur Lösung

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

Multipliziere aus

\frac{3 x + 3}{x ^{2}} : \frac{3}{x} + \frac{3}{x ^{2}}

= \int_{2}^{5} \frac{3}{x} + \frac{3}{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_{2}^{5} \frac{3}{x} d x + \int_{2}^{5} \frac{3}{x ^{2}} d x

\int_{2}^{5} \frac{3}{x} d x = 3 (ln (5) - ln (2))

\int_{2}^{5} \frac{3}{x ^{2}} d x = \frac{9}{10}

= 3 (ln (5) - ln (2)) + \frac{9}{10}

x \to 1 lim (\frac{7 x ^{2} - 4 x - 3}{3 x ^{2} - 4 x + 1})

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