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^{3/2}+7)^6sqrt(x)

Lösung

\int (x^{\frac{3}{2}} + 7)^{6} x d x

Lösung

\frac{2}{21} (x^{\frac{3}{2}} + 7)^{7} + C

Schritte zur Lösung

\int (x^{\frac{3}{2}} + 7)^{6} x d x

Wende U-Substitution an

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

Entferne die Konstante:

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

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

Wende die Potenzregel an

= \frac{2}{3} \cdot \frac{u ^{7}}{7}

Setze in

u = x^{\frac{3}{2}} + 7

ein

= \frac{2}{3} \cdot \frac{( x ^{\frac{3}{2}} + 7 ) ^{7}}{7}

Vereinfache

\frac{2}{3} \cdot \frac{( x ^{\frac{3}{2}} + 7 ) ^{7}}{7} : \frac{2}{21} (x^{\frac{3}{2}} + 7)^{7}

= \frac{2}{21} (x^{\frac{3}{2}} + 7)^{7}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{21} (x^{\frac{3}{2}} + 7)^{7} + C

Graph

Beliebte Beispiele

limit as x approaches 5 of 2

x \to 5 lim (2)

tangent x^2-x^4

t an g e n t x^{2} - x^{4}

integral of e^{-6x^2}

\int e^{- 6 x^{2}} d x

integral of ((ln(x))/x)

\int (\frac{ln ( x )}{x}) d x

limit as x approaches infinity of 6x^4

x \to \infty lim (6 x^{4})