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Beliebt Rechnen >

integral of (16s-4)/(3-2s+4s^2)

Lösung

\int \frac{16 s - 4}{3 - 2 s + 4 s ^{2}} d s

Lösung

2 ln 16 s^{2} - 8 s + 12 + C

Schritte zur Lösung

\int \frac{16 s - 4}{3 - 2 s + 4 s ^{2}} d s

Multipliziere aus

\frac{16 s - 4}{3 - 2 s + 4 s ^{2}} : \frac{16 s}{3 - 2 s + 4 s ^{2}} - \frac{4}{3 - 2 s + 4 s ^{2}}

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{16 s}{3 - 2 s + 4 s ^{2}} d s - \int \frac{4}{3 - 2 s + 4 s ^{2}} d s

\int \frac{16 s}{3 - 2 s + 4 s ^{2}} d s = 16 (\frac{1}{8} ln 16 s^{2} - 8 s + 12 + \frac{1}{4 11} arctan (\frac{4 s - 1}{11}))

\int \frac{4}{3 - 2 s + 4 s ^{2}} d s = \frac{4}{11} arctan (\frac{4 s - 1}{11})

= 16 (\frac{1}{8} ln 16 s^{2} - 8 s + 12 + \frac{1}{4 11} arctan (\frac{4 s - 1}{11})) - \frac{4}{11} arctan (\frac{4 s - 1}{11})

Vereinfache

16 (\frac{1}{8} ln 16 s^{2} - 8 s + 12 + \frac{1}{4 11} arctan (\frac{4 s - 1}{11})) - \frac{4}{11} arctan (\frac{4 s - 1}{11}) : 2 ln 16 s^{2} - 8 s + 12

= 2 ln 16 s^{2} - 8 s + 12

Füge eine Konstante zur Lösung hinzu

= 2 ln 16 s^{2} - 8 s + 12 + C

Graph

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