integral of (5x^2+7x^{-2})

Lösung

\int (5 x^{2} + 7 x^{- 2}) d x

\frac{5 x ^{3}}{3} - \frac{7}{x} + C

Schritte zur Lösung

\int 5 x^{2} + 7 x^{- 2} d x

7 x^{- 2} = \frac{7}{x ^{2}}

= \int 5 x^{2} + \frac{7}{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 5 x^{2} d x + \int \frac{7}{x ^{2}} d x

\int 5 x^{2} d x = \frac{5 x ^{3}}{3}

\int \frac{7}{x ^{2}} d x = - \frac{7}{x}

= \frac{5 x ^{3}}{3} - \frac{7}{x}

Füge eine Konstante zur Lösung hinzu

= \frac{5 x ^{3}}{3} - \frac{7}{x} + C

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

\frac{d}{d x} ((x^{4} + 2 x) (x^{3} + 2 x^{2} + 1))

\frac{d}{d x} (\frac{ln ( x )}{1 + ln ( x )})

y^{^{'}} = arctan (\frac{x}{2})

\int x \cdot e^{- 5 x} d x