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Beliebt Rechnen >

integral from 0 to 1 of (x^3)/(x^2-x-6)

Lösung

\int_{0}^{1} \frac{x ^{3}}{x ^{2} - x - 6} d x

Lösung

\frac{3}{2} - \frac{7}{10} ln (\frac{9}{4}) + 6 \cdot \frac{2 ln ( 2 ) - 2 ln ( 3 )}{5}

+1

Dezimale

- 0.04076 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{x ^{3}}{x ^{2} - x - 6} d x

Faktorisiere

\frac{x ^{3}}{x ^{2} - x - 6}

= \int_{0}^{1} \frac{x ^{3}}{( x + 2 ) ( x - 3 )} d x

Lange Division

\frac{x ^{3}}{( x + 2 ) ( x - 3 )} : x + 1 + \frac{7 x + 6}{x ^{2} - x - 6}

= \int_{0}^{1} x + 1 + \frac{7 x + 6}{x ^{2} - x - 6} 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

= \int_{0}^{1} x d x + \int_{0}^{1} 1 d x + \int_{0}^{1} \frac{7 x + 6}{x ^{2} - x - 6} d x

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

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

\int_{0}^{1} \frac{7 x + 6}{x ^{2} - x - 6} d x = - \frac{7}{10} ln (\frac{9}{4}) + 6 \cdot \frac{2 ln ( 2 ) - 2 ln ( 3 )}{5}

= \frac{1}{2} + 1 - \frac{7}{10} ln (\frac{9}{4}) + 6 \cdot \frac{2 ln ( 2 ) - 2 ln ( 3 )}{5}

Ziehe Brüche zusammen

1 + \frac{1}{2} : \frac{3}{2}

= \frac{3}{2} - \frac{7}{10} ln (\frac{9}{4}) + 6 \cdot \frac{2 ln ( 2 ) - 2 ln ( 3 )}{5}

Graph

Beliebte Beispiele

inverselaplace 1/(s^2+40s+2000)

in v erse l a pl a ce \frac{1}{s ^{2} + 40 s + 2000}

8t^2y^{''}-16y=11t^2-1

8 t^{2} y^{^{''}} - 16 y = 11 t^{2} - 1

derivative sqrt(cot(3x))

d er i v a t i v e cot (3 x)

tangent f(x)=2x^3+3x^2-12x+6

t an g e n t f (x) = 2 x^{3} + 3 x^{2} - 12 x + 6

integral of (2x^3)/(\sqrt[3]{x^4-5)}

\int \frac{2 x ^{3}}{3 x ^{4} - 5} d x