integral from e to e^4 of 1/(xsqrt(Inx))

Lösung

\int_{e}^{e^{4}} \frac{1}{x I n x} d x

- \frac{2}{e ^{2} I n} + \frac{2}{e I n}

Schritte zur Lösung

\int_{e}^{e^{4}} \frac{1}{x I n x} d x

Wende U-Substitution an

= \int_{I n e}^{I n e^{4}} \frac{1}{u u} d u

Vereinfache

u u : u^{\frac{3}{2}}

= \int_{I n e}^{I n e^{4}} \frac{1}{u ^{\frac{3}{2}}} d u

Wende die Potenzregel an

= [- \frac{2}{u}]_{I n e}^{I n e^{4}}

Berechne die Grenzen:

- \frac{2}{e ^{2} I n} + \frac{2}{e I n}

= - \frac{2}{e ^{2} I n} + \frac{2}{e I n}

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