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

Lösung

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

2 x^{\frac{1}{2}} + \frac{2}{5} x^{\frac{5}{2}} + C

Schritte zur Lösung

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

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

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

= 2 x^{\frac{1}{2}} + \frac{2}{5} x^{\frac{5}{2}}

Füge eine Konstante zur Lösung hinzu

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

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