de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of 4x(x+1)^3

Lösung

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

Lösung

x (x + 1)^{4} - \frac{1}{5} (x + 1)^{5} + C

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die partielle Integration an

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

\int \frac{1}{4} (x + 1)^{4} d x = \frac{1}{20} (x + 1)^{5}

= 4 (\frac{1}{4} x (x + 1)^{4} - \frac{1}{20} (x + 1)^{5})

Vereinfache

4 (\frac{1}{4} x (x + 1)^{4} - \frac{1}{20} (x + 1)^{5}) : x (x + 1)^{4} - \frac{1}{5} (x + 1)^{5}

= x (x + 1)^{4} - \frac{1}{5} (x + 1)^{5}

Füge eine Konstante zur Lösung hinzu

= x (x + 1)^{4} - \frac{1}{5} (x + 1)^{5} + C

Graph

Beliebte Beispiele

integral of 9/(16+25x^2)

\int \frac{9}{16 + 25 x ^{2}} d x

integral of (x^3-4+5/(x^6))

\int (x^{3} - 4 + \frac{5}{x ^{6}}) d x

integral of 1/((x*ln(x)))

\int \frac{1}{( x \cdot ln ( x ) )} d x

integral of (5x^2-3)4^{3x+1}

\int (5 x^{2} - 3) 4^{3 x + 1} d x

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

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