integral of ((x+6)/(sqrt(x)))

Lösung

\int (\frac{x + 6}{x}) d x

\frac{2}{3} x^{\frac{3}{2}} + 12 x + C

Schritte zur Lösung

\int \frac{x + 6}{x} d x

Multipliziere aus

\frac{x + 6}{x} : x + \frac{6}{x}

= \int x + \frac{6}{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 x d x + \int \frac{6}{x} d x

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

\int \frac{6}{x} d x = 12 x

= \frac{2}{3} x^{\frac{3}{2}} + 12 x

Füge eine Konstante zur Lösung hinzu

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

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t an g e n t f (x) = 5 sec (x), at x = \frac{π}{6}

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