integral from 0 to x of 1/((1-x)^{2.5)}

Lösung

\int_{0}^{x} \frac{1}{( 1 - x ) ^{2.5}} d x

\frac{0.66666 \dots}{( 1 - x ) ^{1.5}} - 0.66666 \dots

Schritte zur Lösung

\int_{0}^{x} \frac{1}{( 1 - x ) ^{2.5}} d x

Wende U-Substitution an

= \int_{1}^{1 - x} - \frac{1}{u ^{2.5}} 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 ^{2.5}} d u

Wende die Potenzregel an

= - [- \frac{0.66666 \dots}{u ^{1.5}}]_{1}^{1 - x}

Berechne die Grenzen:

- \frac{0.66666 \dots}{( 1 - x ) ^{1.5}} + 0.66666 \dots

= - (- \frac{0.66666 \dots}{( 1 - x ) ^{1.5}} + 0.66666 \dots)

Vereinfache

= \frac{0.66666 \dots}{( 1 - x ) ^{1.5}} - 0.66666 \dots

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