integral of x+1/(x^2)

Lösung

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

\frac{x ^{2}}{2} - \frac{1}{x} + C

Schritte zur Lösung

\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

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

Füge eine Konstante zur Lösung hinzu

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

\frac{\partial}{\partial x} (x y - 1)

\frac{\partial}{\partial y} ((x^{2} - 1) (y + 2))

t an g e n t f (x) = \frac{3}{x ^{2}}, at x = 1

\int_{0}^{\frac{π}{4}} 4 sin^{2} (x) d x

h \to 0 lim ((1 + 5 h)^{\frac{1}{h}})