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

Lösung

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

2 x^{\frac{3}{2}} - \frac{2}{5} x^{\frac{5}{2}} + 4 x^{\frac{1}{2}} + C

Schritte zur Lösung

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

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

\int x^{\frac{3}{2}} d x = \frac{2}{5} x^{\frac{5}{2}}

\int 2 x^{- \frac{1}{2}} d x = 4 x^{\frac{1}{2}}

= 2 x^{\frac{3}{2}} - \frac{2}{5} x^{\frac{5}{2}} + 4 x^{\frac{1}{2}}

Füge eine Konstante zur Lösung hinzu

= 2 x^{\frac{3}{2}} - \frac{2}{5} x^{\frac{5}{2}} + 4 x^{\frac{1}{2}} + C

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