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^2+x))/(x^4)

Lösung

\int \frac{( - x ^{2} + x )}{x ^{4}} d x

Lösung

\frac{1}{x} - \frac{1}{2 x ^{2}} + C

Schritte zur Lösung

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

Multipliziere aus

\frac{- x ^{2} + x}{x ^{4}} : - \frac{1}{x ^{2}} + \frac{1}{x ^{3}}

= \int - \frac{1}{x ^{2}} + \frac{1}{x ^{3}} 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 \frac{1}{x ^{2}} d x + \int \frac{1}{x ^{3}} d x

\int \frac{1}{x ^{2}} d x = - \frac{1}{x}

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

= - (- \frac{1}{x}) - \frac{1}{2 x ^{2}}

Vereinfache

= \frac{1}{x} - \frac{1}{2 x ^{2}}

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of (x^8)/(sqrt(x^9-2))

\int \frac{x ^{8}}{x ^{9} - 2} d x

integral of-xcsc^2(x)

\int - x csc^{2} (x) d x

integral of 1/(x^2+y)

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

integral of (2x+3)e^{-2(x^2+3x+1)}

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

integral of (4x+2)/(x^2+1)

\int \frac{4 x + 2}{x ^{2} + 1} d x