integral of (5x+2)/(\sqrt[3]{6x+3)}

Lösung

\int \frac{5 x + 2}{3 6 x + 3} d x

\frac{3 ^{\frac{2}{3}}}{8} (4 x - 3) (2 x + 1)^{\frac{2}{3}} + \frac{1}{2} (6 x + 3)^{\frac{2}{3}} + C

Schritte zur Lösung

\int \frac{5 x + 2}{3 6 x + 3} d x

Multipliziere aus

\frac{5 x + 2}{3 6 x + 3} : \frac{5 x}{3 6 x + 3} + \frac{2}{3 6 x + 3}

= \int \frac{5 x}{3 6 x + 3} + \frac{2}{3 6 x + 3} 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 \frac{5 x}{3 6 x + 3} d x + \int \frac{2}{3 6 x + 3} d x

\int \frac{5 x}{3 6 x + 3} d x = \frac{3 ^{\frac{2}{3}}}{8} (4 x - 3) (2 x + 1)^{\frac{2}{3}}

\int \frac{2}{3 6 x + 3} d x = \frac{1}{2} (6 x + 3)^{\frac{2}{3}}

= \frac{3 ^{\frac{2}{3}}}{8} (4 x - 3) (2 x + 1)^{\frac{2}{3}} + \frac{1}{2} (6 x + 3)^{\frac{2}{3}}

Füge eine Konstante zur Lösung hinzu

= \frac{3 ^{\frac{2}{3}}}{8} (4 x - 3) (2 x + 1)^{\frac{2}{3}} + \frac{1}{2} (6 x + 3)^{\frac{2}{3}} + C

f (x) = \frac{π}{x}

\int \frac{1}{2 x ^{6}} d x

t an g e n t f (x) = - x^{2} - 3 x + 4, at x = - 3

l a pl a ce t r an s f or m e^{- t} sin (t)

x \to 3 lim (f (x))