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Beliebt Rechnen >

integral of x/((x+4)^{1/3)}

Lösung

\int \frac{x}{( x + 4 ) ^{\frac{1}{3}}} d x

Lösung

\frac{3}{5} (x + 4)^{\frac{5}{3}} - 6 (x + 4)^{\frac{2}{3}} + C

Schritte zur Lösung

\int \frac{x}{( x + 4 ) ^{\frac{1}{3}}} d x

Wende U-Substitution an

= \int \frac{u - 4}{u ^{\frac{1}{3}}} d u

Multipliziere aus

\frac{u - 4}{u ^{\frac{1}{3}}} : u^{\frac{2}{3}} - \frac{4}{u ^{\frac{1}{3}}}

= \int u^{\frac{2}{3}} - \frac{4}{u ^{\frac{1}{3}}} 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

= \int u^{\frac{2}{3}} d u - \int \frac{4}{u ^{\frac{1}{3}}} d u

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

\int \frac{4}{u ^{\frac{1}{3}}} d u = 6 u^{\frac{2}{3}}

= \frac{3}{5} u^{\frac{5}{3}} - 6 u^{\frac{2}{3}}

Setze in

u = x + 4

ein

= \frac{3}{5} (x + 4)^{\frac{5}{3}} - 6 (x + 4)^{\frac{2}{3}}

Füge eine Konstante zur Lösung hinzu

= \frac{3}{5} (x + 4)^{\frac{5}{3}} - 6 (x + 4)^{\frac{2}{3}} + C

Graph

Beliebte Beispiele

derivative (8t)/(t^2+9)

d er i v a t i v e \frac{8 t}{t ^{2} + 9}

tangent ((x-1))/((x+1))

t an g e n t \frac{( x - 1 )}{( x + 1 )}

derivative of e^{0.5x^2}

\frac{d}{d x} (e^{0.5 x^{2}})

(\partial)/(\partial y)(x^{-3}y^2+xy^2+3xy)

\frac{\partial}{\partial y} (x^{- 3} y^{2} + x y^{2} + 3 x y)

sum from n=2 to infinity of 5(-3/4)^n

n = 2 \sum \infty 5 (- \frac{3}{4})^{n}