integral of x^{1/2}-3x^{-1/2}

Lösung

\int x^{\frac{1}{2}} - 3 x^{- \frac{1}{2}} d x

\frac{2}{3} x^{\frac{3}{2}} - 6 x^{\frac{1}{2}} + C

Schritte zur Lösung

\int x^{\frac{1}{2}} - 3 x^{- \frac{1}{2}} 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 x^{\frac{1}{2}} d x - \int 3 x^{- \frac{1}{2}} d x

\int x^{\frac{1}{2}} d x = \frac{2}{3} x^{\frac{3}{2}}

\int 3 x^{- \frac{1}{2}} d x = 6 x^{\frac{1}{2}}

= \frac{2}{3} x^{\frac{3}{2}} - 6 x^{\frac{1}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{3} x^{\frac{3}{2}} - 6 x^{\frac{1}{2}} + C

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