integral of (2sqrt(x)-3\sqrt[4]{x})

Lösung

\int (2 x - 3 4 x) d x

\frac{4}{3} x^{\frac{3}{2}} - \frac{12}{5} x^{\frac{5}{4}} + C

Schritte zur Lösung

\int 2 x - 3 4 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 2 x d x - \int 3 4 x d x

\int 2 x d x = \frac{4}{3} x^{\frac{3}{2}}

\int 3 4 x d x = \frac{12}{5} x^{\frac{5}{4}}

= \frac{4}{3} x^{\frac{3}{2}} - \frac{12}{5} x^{\frac{5}{4}}

Füge eine Konstante zur Lösung hinzu

= \frac{4}{3} x^{\frac{3}{2}} - \frac{12}{5} x^{\frac{5}{4}} + C

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