integral from a to b of 1/((x-a)^n)

Lösung

\int_{a}^{b} \frac{1}{( x - a ) ^{n}} d x

\frac{( b - a ) ^{- n + 1}}{- n + 1}

Schritte zur Lösung

\int_{a}^{b} \frac{1}{( x - a ) ^{n}} d x

Wende U-Substitution an

= \int_{0}^{b - a} \frac{1}{u ^{n}} d u

Wende die Potenzregel an

= [\frac{u ^{- n + 1}}{- n + 1}]_{0}^{b - a}

Berechne die Grenzen:

\frac{( b - a ) ^{- n + 1}}{- n + 1}

= \frac{( b - a ) ^{- n + 1}}{- n + 1}

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