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Beliebt Rechnen >

integral from 1 to 6 of (x^2+2)/(7x-x^2)

Lösung

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

Lösung

7 ln (6) + \frac{4 ln ( 6 )}{7} - 5

+1

Dezimale

8.56617 \dots

Schritte zur Lösung

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

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

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

\int_{1}^{6} \frac{7 x + 2}{7 x - x ^{2}} d x = 7 ln (6) + \frac{4 ln ( 6 )}{7}

\int_{1}^{6} 1 d x = 5

= 7 ln (6) + \frac{4 ln ( 6 )}{7} - 5

Graph

Beliebte Beispiele

x + x (y^{^{'}}) 2 - 1 = 0

y^{^{''}} + 2 y^{^{'}} = 3

derivative of y-3x

\frac{d}{d x} (y - 3 x)

derivative of 2x^3+1/(x^2+16x^{7/2}+5)

\frac{d}{d x} (2 x^{3} + \frac{1}{x ^{2}} + 16 x^{\frac{7}{2}} + 5)

2xy^'+y=6x,y(4)=20

2 x y^{^{'}} + y = 6 x, y (4) = 20