de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (z^4)/(\sqrt[3]{6+z^5)}

Lösung

\int \frac{z ^{4}}{3 6 + z ^{5}} d z

Lösung

\frac{3}{10} (6 + z^{5})^{\frac{2}{3}} + C

Schritte zur Lösung

\int \frac{z ^{4}}{3 6 + z ^{5}} d z

Wende U-Substitution an

= \int \frac{1}{5 3 u} d u

Entferne die Konstante:

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

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

Wende die Potenzregel an

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

Setze in

u = 6 + z^{5}

ein

= \frac{1}{5} \cdot \frac{3}{2} (6 + z^{5})^{\frac{2}{3}}

Vereinfache

\frac{1}{5} \cdot \frac{3}{2} (6 + z^{5})^{\frac{2}{3}} : \frac{3}{10} (6 + z^{5})^{\frac{2}{3}}

= \frac{3}{10} (6 + z^{5})^{\frac{2}{3}}

Füge eine Konstante zur Lösung hinzu

= \frac{3}{10} (6 + z^{5})^{\frac{2}{3}} + C

Graph

Beliebte Beispiele

integral of sin^5(3x)*cos^2(3x)

\int sin^{5} (3 x) \cdot cos^{2} (3 x) d x

integral of 2/(sqrt(9-(x+3)^2))

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

integral of x(e^x+1)

\int x (e^{x} + 1) d x

integral of-xy^2

\int - x y^{2} d x

integral of (12)/(x^2+9)

\int \frac{12}{x ^{2} + 9} d x