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Beliebt Rechnen >

integral of 1/(6x^3-7x^2-3x)

Lösung

\int \frac{1}{6 x ^{3} - 7 x ^{2} - 3 x} d x

Lösung

- \frac{1}{3} ln ∣ x ∣ + \frac{3}{11} ln ∣ 3 x + 1 ∣ + \frac{2}{33} ln ∣ 2 x - 3 ∣ + C

Schritte zur Lösung

\int \frac{1}{6 x ^{3} - 7 x ^{2} - 3 x} d x

Ermittle den Partialbruch von

\frac{1}{6 x ^{3} - 7 x ^{2} - 3 x} : - \frac{1}{3 x} + \frac{9}{11 ( 3 x + 1 )} + \frac{4}{33 ( 2 x - 3 )}

= \int - \frac{1}{3 x} + \frac{9}{11 ( 3 x + 1 )} + \frac{4}{33 ( 2 x - 3 )} 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{1}{3 x} d x + \int \frac{9}{11 ( 3 x + 1 )} d x + \int \frac{4}{33 ( 2 x - 3 )} d x

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

\int \frac{9}{11 ( 3 x + 1 )} d x = \frac{3}{11} ln ∣ 3 x + 1 ∣

\int \frac{4}{33 ( 2 x - 3 )} d x = \frac{2}{33} ln ∣ 2 x - 3 ∣

= - \frac{1}{3} ln ∣ x ∣ + \frac{3}{11} ln ∣ 3 x + 1 ∣ + \frac{2}{33} ln ∣ 2 x - 3 ∣

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{3} ln ∣ x ∣ + \frac{3}{11} ln ∣ 3 x + 1 ∣ + \frac{2}{33} ln ∣ 2 x - 3 ∣ + C

Graph

Beliebte Beispiele

y^{^{'}} = 5 y - x y

y^{''}+8y^'+25y=-208*sin(3x)

y^{^{''}} + 8 y^{^{'}} + 25 y = - 208 \cdot sin (3 x)

integral of (5(x-3)^2)/(xsqrt(x))

\int \frac{5 ( x - 3 ) ^{2}}{x x} d x

derivative f(x)= 3/5 x^{15}

d er i v a t i v e f (x) = \frac{3}{5} x^{15}

integral from 0 to 2 of y/(sqrt(25-y^2))

\int_{0}^{2} \frac{y}{25 - y ^{2}} d y