integral from 1 to x of 4/(x^5)

Lösung

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

- \frac{1}{x ^{4}} + 1

Schritte zur Lösung

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Wende die Potenzregel an

= 4 [- \frac{1}{4 x ^{4}}]_{1}^{x}

Berechne die Grenzen:

- \frac{1}{4 x ^{4}} + \frac{1}{4}

= 4 (- \frac{1}{4 x ^{4}} + \frac{1}{4})

Vereinfache

= - \frac{1}{x ^{4}} + 1

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