de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (x^7-2x)/(x^5)

Lösung

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

Lösung

\frac{x ^{3}}{3} + \frac{2}{3 x ^{3}} + C

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

= \frac{x ^{3}}{3} - (- \frac{2}{3 x ^{3}})

Vereinfache

= \frac{x ^{3}}{3} + \frac{2}{3 x ^{3}}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{3} + \frac{2}{3 x ^{3}} + C

Graph

Beliebte Beispiele

integral of sec^2(x)sqrt(1+tan(x))

\int sec^{2} (x) 1 + tan (x) d x

integral of ((2x^2+3))/((x^2+1)^2)

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

integral of (e^{-ax})

\int (e^{- a x}) d x

integral of x^4sqrt(15+x^5)

\int x^{4} 15 + x^{5} d x

integral of (e^t+2)/(e^t+2t)

\int \frac{e ^{t} + 2}{e ^{t} + 2 t} d t