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(1+x^2)^5

Lösung

\int x (1 + x^{2})^{5} d x

Lösung

\frac{1}{12} (1 + x^{2})^{6} + C

Schritte zur Lösung

\int x (1 + x^{2})^{5} d x

Wende U-Substitution an

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

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int u^{5} d u

Wende die Potenzregel an

= \frac{1}{2} \cdot \frac{u ^{6}}{6}

Setze in

u = 1 + x^{2}

ein

= \frac{1}{2} \cdot \frac{( 1 + x ^{2} ) ^{6}}{6}

Vereinfache

\frac{1}{2} \cdot \frac{( 1 + x ^{2} ) ^{6}}{6} : \frac{1}{12} (1 + x^{2})^{6}

= \frac{1}{12} (1 + x^{2})^{6}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{12} (1 + x^{2})^{6} + C

Graph

Beliebte Beispiele

integral of (sin(2x))/(2sin^2(x)+1)

\int \frac{sin ( 2 x )}{2 sin ^{2} ( x ) + 1} d x

integral of (e^{-0.2x})

\int (e^{- 0.2 x}) d x

integral of 5/(x^2-16)

\int \frac{5}{x ^{2} - 16} d x

integral of 10x(1-x)^5

\int 10 x (1 - x)^{5} d x

integral of x^2(7x^3-3)^5

\int x^{2} (7 x^{3} - 3)^{5} d x