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Beliebt Rechnen >

integral of (2x^{-2}+1/(sqrt(x)))

Lösung

\int (2 x^{- 2} + \frac{1}{x}) d x

Lösung

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

Schritte zur Lösung

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

2 x^{- 2} = \frac{2}{x ^{2}}

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

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int \frac{2}{x ^{2}} d x = - \frac{2}{x}

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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