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

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Multipliziere aus

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

= \frac{1}{3} \cdot \int 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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

\frac{\partial}{\partial x} (8 x cos (5 x y))

x \to 0 + lim (\frac{0}{x})

\frac{d y}{d x} = \frac{1}{y + x}

t an g e n t f (x) = x^{2} + 7, at x = 3

\frac{\partial}{\partial y} (- 3 x e^{- x y})