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

Lösung

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

- 2 ln (2)

Dezimale

- 1.38629 \dots

Schritte zur Lösung

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

Multipliziere aus

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

= \int_{1}^{2} 2 x - 3 - \frac{2}{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

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

\int_{1}^{2} 2 x d x = 3

\int_{1}^{2} 3 d x = 3

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

= 3 - 3 - 2 ln (2)

Vereinfache

= - 2 ln (2)

d er i v a t i v e f (x) = \frac{x}{x - 7}

y^{^{''}} + 3 y^{^{'}} + 2 y = \frac{1}{7 + e ^{x}}

\frac{d}{d x} (1 + \frac{1}{2 x})

d er i v a t i v e y = \frac{x - 5}{x + 5}

\frac{d}{d x} ((2 x + 1)^{2} 3 (2 x + 1) + 10)