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

Lösung

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

- 8

Schritte zur Lösung

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

Vereinfache

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

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

\int_{1}^{3} x^{3} d x = 20

\int_{1}^{3} 3 x^{2} d x = 26

\int_{1}^{3} x d x = 4

\int_{1}^{3} 3 d x = 6

= 20 - 26 + 4 - 6

Vereinfache

= - 8

\int_{- 6}^{6} 3 x^{4} d x

\int_{1}^{6} x + 3 d x

\int_{1}^{\infty} \frac{1}{x e ^{x}} d x

\int_{0}^{2} \frac{7 x ^{6}}{2187} d x

\int_{- 3}^{3} (∣ y - 2 ∣)^{3} d y