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Beliebt Rechnen >

integral of (sqrt(x+1))/(x^2)

Lösung

\int \frac{x + 1}{x ^{2}} d x

Lösung

- \frac{x + 1}{x} - \frac{1}{2} ln x + 1 + 1 + \frac{1}{2} ln x + 1 - 1 + C

Schritte zur Lösung

\int \frac{x + 1}{x ^{2}} d x

Wende die partielle Integration an

= - \frac{x + 1}{x} - \int - \frac{1}{2 x x + 1} d x

\int - \frac{1}{2 x x + 1} d x = \frac{1}{2} ln x + 1 + 1 - \frac{1}{2} ln x + 1 - 1

= - \frac{x + 1}{x} - (\frac{1}{2} ln x + 1 + 1 - \frac{1}{2} ln x + 1 - 1)

Vereinfache

= - \frac{x + 1}{x} - \frac{1}{2} ln x + 1 + 1 + \frac{1}{2} ln x + 1 - 1

Füge eine Konstante zur Lösung hinzu

= - \frac{x + 1}{x} - \frac{1}{2} ln x + 1 + 1 + \frac{1}{2} ln x + 1 - 1 + C

Graph

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