integral from 2 to 5 of (4-3x^2)/(x^3)

Lösung

\int_{2}^{5} \frac{4 - 3 x ^{2}}{x ^{3}} d x

\frac{21}{50} - 3 (ln (5) - ln (2))

Dezimale

- 2.32887 \dots

Schritte zur Lösung

\int_{2}^{5} \frac{4 - 3 x ^{2}}{x ^{3}} d x

Multipliziere aus

\frac{4 - 3 x ^{2}}{x ^{3}} : \frac{4}{x ^{3}} - \frac{3}{x}

= \int_{2}^{5} \frac{4}{x ^{3}} - \frac{3}{x} 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{4}{x ^{3}} d x - \int_{2}^{5} \frac{3}{x} d x

\int_{2}^{5} \frac{4}{x ^{3}} d x = \frac{21}{50}

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

= \frac{21}{50} - 3 (ln (5) - ln (2))

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