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Beliebt Rechnen >

integral of (4x+5)/(sqrt(4x+6))

Lösung

\int \frac{4 x + 5}{4 x + 6} d x

Lösung

\frac{2}{3} x 4 x + 6 + \frac{1}{2} 4 x + 6 + C

Schritte zur Lösung

\int \frac{4 x + 5}{4 x + 6} d x

Multipliziere aus

\frac{4 x + 5}{4 x + 6} : \frac{4 x}{4 x + 6} + \frac{5}{4 x + 6}

= \int \frac{4 x}{4 x + 6} + \frac{5}{4 x + 6} 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{4 x}{4 x + 6} d x + \int \frac{5}{4 x + 6} d x

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

\int \frac{5}{4 x + 6} d x = \frac{5}{2} 4 x + 6

= \frac{2}{3} (x - 3) 4 x + 6 + \frac{5}{2} 4 x + 6

Vereinfache

\frac{2}{3} (x - 3) 4 x + 6 + \frac{5}{2} 4 x + 6 : \frac{2}{3} x 4 x + 6 + \frac{1}{2} 4 x + 6

= \frac{2}{3} x 4 x + 6 + \frac{1}{2} 4 x + 6

Füge eine Konstante zur Lösung hinzu

= \frac{2}{3} x 4 x + 6 + \frac{1}{2} 4 x + 6 + C

Graph

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