de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral from 0 to 1 of 3x(x^2-1)^{13}

Lösung

\int_{0}^{1} 3 x (x^{2} - 1)^{13} d x

Lösung

- \frac{3}{28}

+1

Dezimale

- 0.10714 \dots

Schritte zur Lösung

\int_{0}^{1} 3 x (x^{2} - 1)^{13} d x

Entferne die Konstante:

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

= 3 \cdot \int_{0}^{1} x (x^{2} - 1)^{13} d x

Multipliziere aus

x (x^{2} - 1)^{13} : x^{27} - 13 x^{25} + 78 x^{23} - 286 x^{21} + 715 x^{19} - 1287 x^{17} + 1716 x^{15} - 1716 x^{13} + 1287 x^{11} - 715 x^{9} + 286 x^{7} - 78 x^{5} + 13 x^{3} - x

= 3 \cdot \int_{0}^{1} x^{27} - 13 x^{25} + 78 x^{23} - 286 x^{21} + 715 x^{19} - 1287 x^{17} + 1716 x^{15} - 1716 x^{13} + 1287 x^{11} - 715 x^{9} + 286 x^{7} - 78 x^{5} + 13 x^{3} - x d x

Wende die Summenregel an:

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

= 3 (\int_{0}^{1} x^{27} d x - \int_{0}^{1} 13 x^{25} d x + \int_{0}^{1} 78 x^{23} d x - \int_{0}^{1} 286 x^{21} d x + \int_{0}^{1} 715 x^{19} d x - \int_{0}^{1} 1287 x^{17} d x + \int_{0}^{1} 1716 x^{15} d x - \int_{0}^{1} 1716 x^{13} d x + \int_{0}^{1} 1287 x^{11} d x - \int_{0}^{1} 715 x^{9} d x + \int_{0}^{1} 286 x^{7} d x - \int_{0}^{1} 78 x^{5} d x + \int_{0}^{1} 13 x^{3} d x - \int_{0}^{1} x d x)

\int_{0}^{1} x^{27} d x = \frac{1}{28}

\int_{0}^{1} 13 x^{25} d x = \frac{1}{2}

\int_{0}^{1} 78 x^{23} d x = \frac{13}{4}

\int_{0}^{1} 286 x^{21} d x = 13

\int_{0}^{1} 715 x^{19} d x = \frac{143}{4}

\int_{0}^{1} 1287 x^{17} d x = \frac{143}{2}

\int_{0}^{1} 1716 x^{15} d x = \frac{429}{4}

\int_{0}^{1} 1716 x^{13} d x = \frac{858}{7}

\int_{0}^{1} 1287 x^{11} d x = \frac{429}{4}

\int_{0}^{1} 715 x^{9} d x = \frac{143}{2}

\int_{0}^{1} 286 x^{7} d x = \frac{143}{4}

\int_{0}^{1} 78 x^{5} d x = 13

\int_{0}^{1} 13 x^{3} d x = \frac{13}{4}

\int_{0}^{1} x d x = \frac{1}{2}

= 3 (\frac{1}{28} - \frac{1}{2} + \frac{13}{4} - 13 + \frac{143}{4} - \frac{143}{2} + \frac{429}{4} - \frac{858}{7} + \frac{429}{4} - \frac{143}{2} + \frac{143}{4} - 13 + \frac{13}{4} - \frac{1}{2})

Vereinfache

3 (\frac{1}{28} - \frac{1}{2} + \frac{13}{4} - 13 + \frac{143}{4} - \frac{143}{2} + \frac{429}{4} - \frac{858}{7} + \frac{429}{4} - \frac{143}{2} + \frac{143}{4} - 13 + \frac{13}{4} - \frac{1}{2}) : - \frac{3}{28}

= - \frac{3}{28}

Graph

Beliebte Beispiele

integral from x^2 to 2x of 4xy

\int_{x^{2}}^{2 x} 4 x y d y

integral from 0 to pi/4 of sec^4(θ)

\int_{0}^{\frac{π}{4}} sec^{4} (θ) d θ

integral from 1 to 3 of t^2+3t-18

\int_{1}^{3} t^{2} + 3 t - 18 d t

integral from 0 to x^3 of t^2

\int_{0}^{x^{3}} t^{2} d t

integral from-1 to 1 of cos(2pix)

\int_{- 1}^{1} cos (2 π x) d x