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Beliebt Rechnen >

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

Lösung

\int \frac{8 x ^{3} + 8 x ^{2} + 8}{x ^{2} + x} d x

Lösung

4 x^{2} + 8 ln ∣ x ∣ - 8 ln ∣ x + 1 ∣ + C

Schritte zur Lösung

\int \frac{8 x ^{3} + 8 x ^{2} + 8}{x ^{2} + x} d x

Ermittle den Partialbruch von

\frac{8 x ^{3} + 8 x ^{2} + 8}{x ^{2} + x} : 8 x + \frac{8}{x} - \frac{8}{x + 1}

= \int 8 x + \frac{8}{x} - \frac{8}{x + 1} 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 8 x d x + \int \frac{8}{x} d x - \int \frac{8}{x + 1} d x

\int 8 x d x = 4 x^{2}

\int \frac{8}{x} d x = 8 ln ∣ x ∣

\int \frac{8}{x + 1} d x = 8 ln ∣ x + 1 ∣

= 4 x^{2} + 8 ln ∣ x ∣ - 8 ln ∣ x + 1 ∣

Füge eine Konstante zur Lösung hinzu

= 4 x^{2} + 8 ln ∣ x ∣ - 8 ln ∣ x + 1 ∣ + C

Graph

Beliebte Beispiele

integral of (xln(x))/x

\int \frac{x ln ( x )}{x} d x

tangent f(x)= 1/(x^5),(2, 1/32)

t an g e n t f (x) = \frac{1}{x ^{5}}, (2, \frac{1}{32})

derivative f(t)=sqrt(2t^2-t)

d er i v a t i v e f (t) = 2 t^{2} - t

y^'+1/(x+1)y=x^{-2}

y^{^{'}} + \frac{1}{x + 1} y = x^{- 2}

tangent f(x)=(3x-2)(x+4),(1,5)

t an g e n t f (x) = (3 x - 2) (x + 4), (1, 5)