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Beliebt Rechnen >

integral of (1+4x)/(\sqrt[3]{4x+3)}

Lösung

\int \frac{1 + 4 x}{3 4 x + 3} d x

Lösung

\frac{3}{8} (4 x + 3)^{\frac{2}{3}} + \frac{1}{4} (\frac{3}{5} (4 x + 3)^{\frac{5}{3}} - \frac{9}{2} (4 x + 3)^{\frac{2}{3}}) + C

Schritte zur Lösung

\int \frac{1 + 4 x}{3 4 x + 3} d x

Multipliziere aus

\frac{1 + 4 x}{3 4 x + 3} : \frac{1}{3 4 x + 3} + \frac{4 x}{3 4 x + 3}

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

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

\int \frac{4 x}{3 4 x + 3} d x = \frac{1}{4} (\frac{3}{5} (4 x + 3)^{\frac{5}{3}} - \frac{9}{2} (4 x + 3)^{\frac{2}{3}})

= \frac{3}{8} (4 x + 3)^{\frac{2}{3}} + \frac{1}{4} (\frac{3}{5} (4 x + 3)^{\frac{5}{3}} - \frac{9}{2} (4 x + 3)^{\frac{2}{3}})

Füge eine Konstante zur Lösung hinzu

= \frac{3}{8} (4 x + 3)^{\frac{2}{3}} + \frac{1}{4} (\frac{3}{5} (4 x + 3)^{\frac{5}{3}} - \frac{9}{2} (4 x + 3)^{\frac{2}{3}}) + C

Graph

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