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Beliebt Rechnen >

integral of (5x-x)/(sqrt(3x^2-9))

Lösung

\int \frac{5 x - x}{3 x ^{2} - 9} d x

Lösung

\frac{4}{3} 3 x^{2} - 9 + C

Schritte zur Lösung

\int \frac{5 x - x}{3 x ^{2} - 9} d x

Multipliziere aus

\frac{5 x - x}{3 x ^{2} - 9} : \frac{5 x}{3 x ^{2} - 9} - \frac{x}{3 x ^{2} - 9}

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 x ^{2} - 9} d x - \int \frac{x}{3 x ^{2} - 9} d x

\int \frac{5 x}{3 x ^{2} - 9} d x = \frac{5}{3} 3 x^{2} - 9

\int \frac{x}{3 x ^{2} - 9} d x = \frac{1}{3} 3 x^{2} - 9

= \frac{5}{3} 3 x^{2} - 9 - \frac{1}{3} 3 x^{2} - 9

Vereinfache

\frac{5}{3} 3 x^{2} - 9 - \frac{1}{3} 3 x^{2} - 9 : \frac{4}{3} 3 x^{2} - 9

= \frac{4}{3} 3 x^{2} - 9

Füge eine Konstante zur Lösung hinzu

= \frac{4}{3} 3 x^{2} - 9 + C

Graph

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