integral of [5x+2/(3x^5)]

Lösung

\int [5 x + \frac{2}{3 x ^{5}}] d x

\frac{5 x ^{2}}{2} - \frac{1}{6 x ^{4}} + C

Schritte zur Lösung

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

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

\int \frac{2}{3 x ^{5}} d x = - \frac{1}{6 x ^{4}}

= \frac{5 x ^{2}}{2} - \frac{1}{6 x ^{4}}

Füge eine Konstante zur Lösung hinzu

= \frac{5 x ^{2}}{2} - \frac{1}{6 x ^{4}} + C

d er i v a t i v e 2 a x + \frac{b}{x}

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

\frac{d}{d x} (e^{2 x} - x^{2} - 1)

x \to 4 lim (4 - x)

\int_{1}^{3} \frac{x}{x ^{2} + 6 x + 13} d x