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Beliebt Rechnen >

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

Lösung

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

Lösung

- 1 + 7 ln (2)

+1

Dezimale

3.85203 \dots

Schritte zur Lösung

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

Faktorisiere

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

= \int_{1}^{2} \frac{x ^{2} + 6}{- x ( x - 3 )} d x

Entferne die Konstante:

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

= - \int_{1}^{2} \frac{x ^{2} + 6}{x ( x - 3 )} d x

Multipliziere aus

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

Wende die Summenregel an:

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

= - (\int_{1}^{2} \frac{x ^{2}}{x ( x - 3 )} d x + \int_{1}^{2} \frac{6}{x ( x - 3 )} d x)

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

\int_{1}^{2} \frac{6}{x ( x - 3 )} d x = - 4 ln (2)

= - (1 - 3 ln (2) - 4 ln (2))

Vereinfache

= - 1 + 7 ln (2)

Graph

Beliebte Beispiele

integral of sqrt(7x+9)

\int 7 x + 9 d x

integral from 1 to 4 of x^2+1

\int_{1}^{4} x^{2} + 1 d x

derivative e^{2x^3}

d er i v a t i v e e^{2 x^{3}}

integral of sin^2(2x)cos(2x)

\int sin^{2} (2 x) cos (2 x) d x

derivative (x^2)/(3x+7)

d er i v a t i v e \frac{x ^{2}}{3 x + 7}