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Beliebt >

integral of (3/(2x-1)+5/(3x-4))

Lösung

\int (\frac{3}{2 x - 1} + \frac{5}{3 x - 4}) d x

Lösung

\frac{3}{2} ln ∣ 2 x - 1 ∣ + \frac{5}{3} ln ∣ 3 x - 4 ∣ + C

Schritte zur Lösung

\int \frac{3}{2 x - 1} + \frac{5}{3 x - 4} 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{3}{2 x - 1} d x + \int \frac{5}{3 x - 4} d x

\int \frac{3}{2 x - 1} d x = \frac{3}{2} ln ∣ 2 x - 1 ∣

\int \frac{5}{3 x - 4} d x = \frac{5}{3} ln ∣ 3 x - 4 ∣

= \frac{3}{2} ln ∣ 2 x - 1 ∣ + \frac{5}{3} ln ∣ 3 x - 4 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{3}{2} ln ∣ 2 x - 1 ∣ + \frac{5}{3} ln ∣ 3 x - 4 ∣ + C

Beliebte Beispiele

integral of (4x^2+3+8/(x^2+1))

\int (4 x^{2} + 3 + \frac{8}{x ^{2} + 1}) d x

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

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

integral of sqrt(2-3x^2)

\int 2 - 3 x^{2} d x

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

\int \frac{x + 2}{x ^{2} + 2 x + 1} d x

integral of (2x-1)sqrt(x+3)

\int (2 x - 1) x + 3 d x