integral from 1 to 2^n of x^{n-1}

Lösung

\int_{1}^{2^{n}} x^{n - 1} d x

\frac{2 ^{n^{2}} - 1}{n}

Schritte zur Lösung

\int_{1}^{2^{n}} x^{n - 1} d x

Wende die Potenzregel an

= [\frac{x ^{n}}{n}]_{1}^{2^{n}}

Berechne die Grenzen:

\frac{2 ^{n^{2}}}{n} - \frac{1}{n}

= \frac{2 ^{n^{2}}}{n} - \frac{1}{n}

Vereinfache

= \frac{2 ^{n^{2}} - 1}{n}

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