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

Lösung

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

\frac{x ^{2}}{2} + 2 x + \frac{4}{x} + C

Schritte zur Lösung

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

Multipliziere aus

\frac{x ^{3} + 2 x ^{2} - 4}{x ^{2}} : x + 2 - \frac{4}{x ^{2}}

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

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

\int 2 d x = 2 x

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

= \frac{x ^{2}}{2} + 2 x - (- \frac{4}{x})

Vereinfache

= \frac{x ^{2}}{2} + 2 x + \frac{4}{x}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{2} + 2 x + \frac{4}{x} + C

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

x \to 0 lim (ln (e^{x} - 1))

t an g e n t \frac{1}{( x - 1 )}, at x = 2

x \to 1 + lim (\frac{x}{x ^{2} - 1})

\frac{\partial}{\partial v} ((u^{2} v - v^{3})^{5})