integral of ((x^7-4x^5+11)/(x^5))

Lösung

\int (\frac{x ^{7} - 4 x ^{5} + 11}{x ^{5}}) d x

\frac{x ^{3}}{3} - 4 x - \frac{11}{4 x ^{4}} + C

Schritte zur Lösung

\int \frac{x ^{7} - 4 x ^{5} + 11}{x ^{5}} d x

Multipliziere aus

\frac{x ^{7} - 4 x ^{5} + 11}{x ^{5}} : x^{2} - 4 + \frac{11}{x ^{5}}

= \int x^{2} - 4 + \frac{11}{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 x^{2} d x - \int 4 d x + \int \frac{11}{x ^{5}} d x

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

\int 4 d x = 4 x

\int \frac{11}{x ^{5}} d x = - \frac{11}{4 x ^{4}}

= \frac{x ^{3}}{3} - 4 x - \frac{11}{4 x ^{4}}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{3} - 4 x - \frac{11}{4 x ^{4}} + C

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

x \to 1 lim ((1 - 2 x)^{\frac{1}{x}})

d er i v a t i v e f (x) = \frac{t ^{3} + 3 t}{t ^{3 - 4 t + 3}}

\frac{\partial}{\partial x} (3 sec^{2} (2 x + 3 y))

\int \frac{e ^{x}}{4 - e ^{x}} d x