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

Lösung

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

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

Schritte zur Lösung

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

Multipliziere aus

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

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

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

\int 3 d x = 3 x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

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

= \frac{x ^{2}}{2} - 3 x + 3 ln ∣ x ∣ - (- \frac{1}{x})

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

l a pl a ce t r an s f or m g (t) = 4 cos (4 t) - 9 sin (4 t) + 2 cos (10 t)

\frac{\partial}{\partial x} (r sin (t) sin (x))

\frac{\partial}{\partial x} (e^{- (x^{2} + y^{2} + 2 z^{2})})

\int \frac{3}{x} + \frac{x x}{4} + C d x

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