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^7-5x)/(x^6)

Lösung

\int \frac{x ^{7} - 5 x}{x ^{6}} d x

Lösung

\frac{x ^{2}}{2} + \frac{5}{4 x ^{4}} + C

Schritte zur Lösung

\int \frac{x ^{7} - 5 x}{x ^{6}} d x

Multipliziere aus

\frac{x ^{7} - 5 x}{x ^{6}} : x - \frac{5}{x ^{5}}

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

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

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

= \frac{x ^{2}}{2} - (- \frac{5}{4 x ^{4}})

Vereinfache

= \frac{x ^{2}}{2} + \frac{5}{4 x ^{4}}

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of 2xsin(npix)

\int 2 x sin (nπ x) d x

integral of 1/(sqrt(x+6x^2))

\int \frac{1}{x + 6 x ^{2}} d x

integral of (2e^x+6/x+5)

\int (2 e^{x} + \frac{6}{x} + 5) d x

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

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

integral of 7/3 cos(1/3 x)-2sin(2/3 x)

\int \frac{7}{3} cos (\frac{1}{3} x) - 2 sin (\frac{2}{3} x) d x