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^9sqrt(x^5+2)

Lösung

\int x^{9} x^{5} + 2 d x

Lösung

\frac{1}{5} (\frac{2}{5} (x^{5} + 2)^{\frac{5}{2}} - \frac{4}{3} (x^{5} + 2)^{\frac{3}{2}}) + C

Schritte zur Lösung

\int x^{9} x^{5} + 2 d x

Wende U-Substitution an

= \int \frac{( u - 2 ) u}{5} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{5} \cdot \int (u - 2) u d u

Multipliziere aus

(u - 2) u : u^{\frac{3}{2}} - 2 u

= \frac{1}{5} \cdot \int u^{\frac{3}{2}} - 2 u d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{5} (\int u^{\frac{3}{2}} d u - \int 2 u d u)

\int u^{\frac{3}{2}} d u = \frac{2}{5} u^{\frac{5}{2}}

\int 2 u d u = \frac{4}{3} u^{\frac{3}{2}}

= \frac{1}{5} (\frac{2}{5} u^{\frac{5}{2}} - \frac{4}{3} u^{\frac{3}{2}})

Setze in

u = x^{5} + 2

ein

= \frac{1}{5} (\frac{2}{5} (x^{5} + 2)^{\frac{5}{2}} - \frac{4}{3} (x^{5} + 2)^{\frac{3}{2}})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{5} (\frac{2}{5} (x^{5} + 2)^{\frac{5}{2}} - \frac{4}{3} (x^{5} + 2)^{\frac{3}{2}}) + C

Graph

Beliebte Beispiele

xy^'-y^2ln(x)+y=0

x y^{^{'}} - y^{2} ln (x) + y = 0

limit as x approaches 3 of 7x-6

x \to 3 lim (7 x - 6)

derivative sin(x)

d er i v a t i v e sin (x)

(\partial)/(\partial x)(1000-4xy+xy^2)

\frac{\partial}{\partial x} (1000 - 4 x y + x y^{2})

(dy)/(dx)=(2x)/((1+x^2))

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