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})

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

\int ln (5^{x}) d x

d er i v a t i v e 9 t^{2} + t^{3}

\frac{d}{d x} (lo g_{10} (2 x - 3))

\int \frac{x ^{2} + 12 x - 4}{x ^{3} - 4 x} d x

\frac{\partial}{\partial x} (4 x ln (y) + y ln (z) - 4 x)