integral from 0 to x of 1/((1-x)^{0.4)}

Lösung

\int_{0}^{x} \frac{1}{( 1 - x ) ^{0.4}} d x

- 1.66666 \dots (1 - x)^{0.6} + 1.66666 \dots

Schritte zur Lösung

\int_{0}^{x} \frac{1}{( 1 - x ) ^{0.4}} d x

Wende U-Substitution an

= \int_{1}^{1 - x} - \frac{1}{u ^{0.4}} d u

Entferne die Konstante:

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

= - \int_{1}^{1 - x} \frac{1}{u ^{0.4}} d u

Wende die Potenzregel an

= - [1.66666 \dots u^{0.6}]_{1}^{1 - x}

Berechne die Grenzen:

1.66666 \dots (1 - x)^{0.6} - 1.66666 \dots

= - (1.66666 \dots (1 - x)^{0.6} - 1.66666 \dots)

Vereinfache

= - 1.66666 \dots (1 - x)^{0.6} + 1.66666 \dots

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