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+5))/(\sqrt[3]{x+9)}

Lösung

\int \frac{( x + 5 )}{3 x + 9} d x

Lösung

\frac{3}{5} (x + 9)^{\frac{5}{3}} - 6 (x + 9)^{\frac{2}{3}} + C

Schritte zur Lösung

\int \frac{x + 5}{3 x + 9} d x

Multipliziere aus

\frac{x + 5}{3 x + 9} : \frac{x}{3 x + 9} + \frac{5}{3 x + 9}

= \int \frac{x}{3 x + 9} + \frac{5}{3 x + 9} 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{x}{3 x + 9} d x + \int \frac{5}{3 x + 9} d x

\int \frac{x}{3 x + 9} d x = \frac{3}{5} (x + 9)^{\frac{5}{3}} - \frac{27}{2} (x + 9)^{\frac{2}{3}}

\int \frac{5}{3 x + 9} d x = \frac{15}{2} (x + 9)^{\frac{2}{3}}

= \frac{3}{5} (x + 9)^{\frac{5}{3}} - \frac{27}{2} (x + 9)^{\frac{2}{3}} + \frac{15}{2} (x + 9)^{\frac{2}{3}}

Addiere gleiche Elemente:

- \frac{27}{2} (x + 9)^{\frac{2}{3}} + \frac{15}{2} (x + 9)^{\frac{2}{3}} = - 6 (x + 9)^{\frac{2}{3}}

= \frac{3}{5} (x + 9)^{\frac{5}{3}} - 6 (x + 9)^{\frac{2}{3}}

Füge eine Konstante zur Lösung hinzu

= \frac{3}{5} (x + 9)^{\frac{5}{3}} - 6 (x + 9)^{\frac{2}{3}} + C

Graph

Beliebte Beispiele

tangent f(x)=sqrt(9-x),\at x=0

t an g e n t f (x) = 9 - x, at x = 0

limit as x approaches-1 of 3x^2+2x-1

x \to - 1 lim (3 x^{2} + 2 x - 1)

inverselaplace 6/(s^2(7s+1))

in v erse l a pl a ce \frac{6}{s ^{2} ( 7 s + 1 )}

integral of 10x(4x^2-1)^9

\int 10 x (4 x^{2} - 1)^{9} d x

taylor ln(-2x-5),-5

t a y l or ln (- 2 x - 5), - 5