de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (1/(\sqrt[3]{x)+sqrt(x)})

Lösung

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

Lösung

6 (\frac{( 1 + 6 x ) ^{3}}{3} - \frac{3 ( 1 + 6 x ) ^{2}}{2} + 3 (1 + 6 x) - ln 1 + 6 x) + C

Schritte zur Lösung

\int \frac{1}{3 x + x} d x

Wende U-Substitution an

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

Entferne die Konstante:

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

= 6 \cdot \int \frac{u ^{3}}{1 + u} d u

Wende U-Substitution an

= 6 \cdot \int \frac{( v - 1 ) ^{3}}{v} d v

Multipliziere aus

\frac{( v - 1 ) ^{3}}{v} : v^{2} - 3 v + 3 - \frac{1}{v}

= 6 \cdot \int v^{2} - 3 v + 3 - \frac{1}{v} d v

Wende die Summenregel an:

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

= 6 (\int v^{2} d v - \int 3 v d v + \int 3 d v - \int \frac{1}{v} d v)

\int v^{2} d v = \frac{v ^{3}}{3}

\int 3 v d v = \frac{3 v ^{2}}{2}

\int 3 d v = 3 v

\int \frac{1}{v} d v = ln ∣ v ∣

= 6 (\frac{v ^{3}}{3} - \frac{3 v ^{2}}{2} + 3 v - ln ∣ v ∣)

Ersetze zurück

= 6 (\frac{( 1 + 6 x ) ^{3}}{3} - \frac{3 ( 1 + 6 x ) ^{2}}{2} + 3 (1 + 6 x) - ln 1 + 6 x)

Füge eine Konstante zur Lösung hinzu

= 6 (\frac{( 1 + 6 x ) ^{3}}{3} - \frac{3 ( 1 + 6 x ) ^{2}}{2} + 3 (1 + 6 x) - ln 1 + 6 x) + C

Graph

Beliebte Beispiele

integral of xsqrt(3-x^2)-x^2

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

integral of x/(sqrt(3x+2))

\int \frac{x}{3 x + 2} d x

(\partial)/(\partial x)(e^{yln(z)})

\frac{\partial}{\partial x} (e^{y l n (z)})

derivative 9/(t^3)

d er i v a t i v e \frac{9}{t ^{3}}

integral from-pi to pi of tsin(nt)

\int_{- π}^{π} t sin (n t) d t