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

Lösung

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

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

Schritte zur Lösung

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

Multipliziere aus

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

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

\int 1 d x = x

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

= x - \frac{2}{x}

Füge eine Konstante zur Lösung hinzu

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

\int_{2}^{4} \frac{1}{x ( ln ( x ) ) ^{2}} d x

\int_{1}^{3} \frac{3}{x ^{2}} d x

\int \frac{x ^{4}}{( 3 - x ^{5} ) ^{2}} d x

\int \frac{1}{( x - 6 ) ( x - 3 )} d x

\frac{\partial}{\partial x} (\frac{93}{2 + x ^{2} + y ^{2}})