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Beliebt Rechnen >

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

Lösung

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

Lösung

ln ∣ x ∣ - \frac{4}{x ^{2}} + C

Schritte zur Lösung

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

Multipliziere aus

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

= \int \frac{1}{x} + \frac{8}{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}{x} d x + \int \frac{8}{x ^{3}} d x

\int \frac{1}{x} d x = ln ∣ x ∣

\int \frac{8}{x ^{3}} d x = - \frac{4}{x ^{2}}

= ln ∣ x ∣ - \frac{4}{x ^{2}}

Füge eine Konstante zur Lösung hinzu

= ln ∣ x ∣ - \frac{4}{x ^{2}} + C

Graph

Beliebte Beispiele

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

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

integral of 1/((x^3))

\int \frac{1}{( x ^{3} )} d x

integral of (4x^2+10x+13)/((x+2)(x^2+5))

\int \frac{4 x ^{2} + 10 x + 13}{( x + 2 ) ( x ^{2} + 5 )} d x

integral of (4pix+4pi)/(x^2-4x+8)

\int \frac{4 π x + 4 π}{x ^{2} - 4 x + 8} d x

integral of 9/(xln(5x))

\int \frac{9}{x ln ( 5 x )} d x