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Beliebt Rechnen >

integral of ((sqrt(x)+1))/(\sqrt[4]{x)}

Lösung

\int \frac{( x + 1 )}{4 x} d x

Lösung

\frac{4}{5} x^{\frac{5}{4}} + \frac{4}{3} x^{\frac{3}{4}} + C

Schritte zur Lösung

\int \frac{x + 1}{4 x} d x

Multipliziere aus

\frac{x + 1}{4 x} : 4 x + \frac{1}{4 x}

= \int 4 x + \frac{1}{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 4 x d x + \int \frac{1}{4 x} d x

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

\int \frac{1}{4 x} d x = \frac{4}{3} x^{\frac{3}{4}}

= \frac{4}{5} x^{\frac{5}{4}} + \frac{4}{3} x^{\frac{3}{4}}

Füge eine Konstante zur Lösung hinzu

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

Graph

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