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Beliebt Rechnen >

integral of (5x-4)/(sqrt(8x-5^2+9))

Lösung

\int \frac{5 x - 4}{8 x - 5 ^{2} + 9} d x

Lösung

\frac{5}{12} x 8 x - 16 + \frac{2}{3} 8 x - 16 + C

Schritte zur Lösung

\int \frac{5 x - 4}{8 x - 5 ^{2} + 9} d x

Multipliziere aus

\frac{5 x - 4}{8 x - 5 ^{2} + 9} : \frac{5 x}{8 x - 16} - \frac{4}{8 x - 16}

= \int \frac{5 x}{8 x - 16} - \frac{4}{8 x - 16} 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}{8 x - 16} d x - \int \frac{4}{8 x - 16} d x

\int \frac{5 x}{8 x - 16} d x = \frac{5}{12} (x + 4) 8 x - 16

\int \frac{4}{8 x - 16} d x = 8 x - 16

= \frac{5}{12} (x + 4) 8 x - 16 - 8 x - 16

Vereinfache

\frac{5}{12} (x + 4) 8 x - 16 - 8 x - 16 : \frac{5}{12} x 8 x - 16 + \frac{2}{3} 8 x - 16

= \frac{5}{12} x 8 x - 16 + \frac{2}{3} 8 x - 16

Füge eine Konstante zur Lösung hinzu

= \frac{5}{12} x 8 x - 16 + \frac{2}{3} 8 x - 16 + C

Graph

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