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Beliebt Rechnen >

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

Lösung

\int \frac{( 1 - 3 x ) ^{2}}{x ^{3}} d x

Lösung

- \frac{1}{2 x ^{2}} + \frac{6}{x} + 9 ln ∣ x ∣ + C

Schritte zur Lösung

\int \frac{( 1 - 3 x ) ^{2}}{x ^{3}} d x

Multipliziere aus

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

= \int \frac{1}{x ^{3}} - \frac{6}{x ^{2}} + \frac{9}{x} 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 ^{3}} d x - \int \frac{6}{x ^{2}} d x + \int \frac{9}{x} d x

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

\int \frac{6}{x ^{2}} d x = - \frac{6}{x}

\int \frac{9}{x} d x = 9 ln ∣ x ∣

= - \frac{1}{2 x ^{2}} - (- \frac{6}{x}) + 9 ln ∣ x ∣

Vereinfache

= - \frac{1}{2 x ^{2}} + \frac{6}{x} + 9 ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{2 x ^{2}} + \frac{6}{x} + 9 ln ∣ x ∣ + C

Graph

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