integral from 1 to 5 of (x^3-1)/(x^3)

Lösung

\int_{1}^{5} \frac{x ^{3} - 1}{x ^{3}} d x

\frac{88}{25}

Dezimale

3.52

Schritte zur Lösung

\int_{1}^{5} \frac{x ^{3} - 1}{x ^{3}} d x

Multipliziere aus

\frac{x ^{3} - 1}{x ^{3}} : 1 - \frac{1}{x ^{3}}

= \int_{1}^{5} 1 - \frac{1}{x ^{3}} 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 ^{3}} d x

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

\int_{1}^{5} \frac{1}{x ^{3}} d x = \frac{12}{25}

= 4 - \frac{12}{25}

Vereinfache

4 - \frac{12}{25} : \frac{88}{25}

= \frac{88}{25}

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