integral of (99x-83)/(121x^2-176x+64)

Lösung

\int \frac{99 x - 83}{121 x ^{2} - 176 x + 64} d x

\frac{9 ( ln ( \frac{1}{11} ∣ 11 x - 8 ∣ ) ( 11 x - 8 ) - 8 )}{11 ( 11 x - 8 )} + \frac{83}{11 ( 11 x - 8 )} + C

Schritte zur Lösung

\int \frac{99 x - 83}{121 x ^{2} - 176 x + 64} d x

Multipliziere aus

\frac{99 x - 83}{121 x ^{2} - 176 x + 64} : \frac{99 x}{121 x ^{2} - 176 x + 64} - \frac{83}{121 x ^{2} - 176 x + 64}

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{99 x}{121 x ^{2} - 176 x + 64} d x - \int \frac{83}{121 x ^{2} - 176 x + 64} d x

\int \frac{99 x}{121 x ^{2} - 176 x + 64} d x = \frac{9 ( ln ( \frac{1}{11} ∣ 11 x - 8 ∣ ) ( 11 x - 8 ) - 8 )}{11 ( 11 x - 8 )}

\int \frac{83}{121 x ^{2} - 176 x + 64} d x = - \frac{83}{11 ( 11 x - 8 )}

= \frac{9 ( ln ( \frac{1}{11} ∣ 11 x - 8 ∣ ) ( 11 x - 8 ) - 8 )}{11 ( 11 x - 8 )} - (- \frac{83}{11 ( 11 x - 8 )})

Vereinfache

= \frac{9 ( ln ( \frac{1}{11} ∣ 11 x - 8 ∣ ) ( 11 x - 8 ) - 8 )}{11 ( 11 x - 8 )} + \frac{83}{11 ( 11 x - 8 )}

Füge eine Konstante zur Lösung hinzu

= \frac{9 ( ln ( \frac{1}{11} ∣ 11 x - 8 ∣ ) ( 11 x - 8 ) - 8 )}{11 ( 11 x - 8 )} + \frac{83}{11 ( 11 x - 8 )} + C

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