integral from 2 to e of (x^4-3x)/(x^2)

Lösung

\int_{2}^{e} \frac{x ^{4} - 3 x}{x ^{2}} d x

\frac{e ^{3} - 8}{3} - 3 (1 - ln (2))

Dezimale

3.10795 \dots

Schritte zur Lösung

\int_{2}^{e} \frac{x ^{4} - 3 x}{x ^{2}} d x

Multipliziere aus

\frac{x ^{4} - 3 x}{x ^{2}} : x^{2} - \frac{3}{x}

= \int_{2}^{e} x^{2} - \frac{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

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

\int_{2}^{e} x^{2} d x = \frac{e ^{3} - 8}{3}

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

= \frac{e ^{3} - 8}{3} - 3 (1 - ln (2))