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Beliebt Rechnen >

integral of (-10x+2)/((-2x+1)^2)

Lösung

\int \frac{- 10 x + 2}{( - 2 x + 1 ) ^{2}} d x

Lösung

- \frac{5}{2} (ln ∣ - 2 x + 1 ∣ + \frac{1}{- 2 x + 1}) + \frac{1}{- 2 x + 1} + C

Schritte zur Lösung

\int \frac{- 10 x + 2}{( - 2 x + 1 ) ^{2}} d x

Multipliziere aus

\frac{- 10 x + 2}{( - 2 x + 1 ) ^{2}} : - \frac{10 x}{( - 2 x + 1 ) ^{2}} + \frac{2}{( - 2 x + 1 ) ^{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{10 x}{( - 2 x + 1 ) ^{2}} d x + \int \frac{2}{( - 2 x + 1 ) ^{2}} d x

\int \frac{10 x}{( - 2 x + 1 ) ^{2}} d x = \frac{5}{2} (ln ∣ - 2 x + 1 ∣ + \frac{1}{- 2 x + 1})

\int \frac{2}{( - 2 x + 1 ) ^{2}} d x = \frac{1}{- 2 x + 1}

= - \frac{5}{2} (ln ∣ - 2 x + 1 ∣ + \frac{1}{- 2 x + 1}) + \frac{1}{- 2 x + 1}

Füge eine Konstante zur Lösung hinzu

= - \frac{5}{2} (ln ∣ - 2 x + 1 ∣ + \frac{1}{- 2 x + 1}) + \frac{1}{- 2 x + 1} + C

Graph

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