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Beliebt Rechnen >

integral of (-13x+3)/((-4x+2)^2)

Lösung

\int \frac{- 13 x + 3}{( - 4 x + 2 ) ^{2}} d x

Lösung

- 13 (\frac{x}{4 ( - 4 x + 2 )} + \frac{1}{16} ln ∣ - 4 x + 2 ∣) + \frac{3}{4 ( - 4 x + 2 )} + C

Schritte zur Lösung

\int \frac{- 13 x + 3}{( - 4 x + 2 ) ^{2}} d x

Multipliziere aus

\frac{- 13 x + 3}{( - 4 x + 2 ) ^{2}} : - \frac{13 x}{( - 4 x + 2 ) ^{2}} + \frac{3}{( - 4 x + 2 ) ^{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{13 x}{( - 4 x + 2 ) ^{2}} d x + \int \frac{3}{( - 4 x + 2 ) ^{2}} d x

\int \frac{13 x}{( - 4 x + 2 ) ^{2}} d x = 13 (\frac{x}{4 ( - 4 x + 2 )} + \frac{1}{16} ln ∣ - 4 x + 2 ∣)

\int \frac{3}{( - 4 x + 2 ) ^{2}} d x = \frac{3}{4 ( - 4 x + 2 )}

= - 13 (\frac{x}{4 ( - 4 x + 2 )} + \frac{1}{16} ln ∣ - 4 x + 2 ∣) + \frac{3}{4 ( - 4 x + 2 )}

Füge eine Konstante zur Lösung hinzu

= - 13 (\frac{x}{4 ( - 4 x + 2 )} + \frac{1}{16} ln ∣ - 4 x + 2 ∣) + \frac{3}{4 ( - 4 x + 2 )} + C

Graph

Beliebte Beispiele

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