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+3x^5-2x^3-4)/(x^3)

Lösung

\int \frac{x ^{7} + 3 x ^{5} - 2 x ^{3} - 4}{x ^{3}} d x

Lösung

\frac{x ^{5}}{5} + x^{3} - 2 x + \frac{2}{x ^{2}} + C

Schritte zur Lösung

\int \frac{x ^{7} + 3 x ^{5} - 2 x ^{3} - 4}{x ^{3}} d x

Multipliziere aus

\frac{x ^{7} + 3 x ^{5} - 2 x ^{3} - 4}{x ^{3}} : x^{4} + 3 x^{2} - 2 - \frac{4}{x ^{3}}

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

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

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

\int 2 d x = 2 x

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

= \frac{x ^{5}}{5} + x^{3} - 2 x - (- \frac{2}{x ^{2}})

Vereinfache

= \frac{x ^{5}}{5} + x^{3} - 2 x + \frac{2}{x ^{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{5}}{5} + x^{3} - 2 x + \frac{2}{x ^{2}} + C

Graph

Beliebte Beispiele

derivative of (e^{1-cos(x})/(cos(x)))

\frac{d}{d x} (\frac{e ^{1 - c o s (x)}}{cos ( x )})

d/(du)(sqrt(cos(c)(cot(u))))

\frac{d}{d u} (cos (c) (cot (u)))

y^{^{'}} = e^{2 x + y}

integral of 5/(5+e^x)

\int \frac{5}{5 + e ^{x}} d x

(\partial)/(\partial x)(ln(1-e^{-x}))

\frac{\partial}{\partial x} (ln (1 - e^{- x}))