integral from 1 to 3 of ((x^2+5)/x)

Lösung

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

4 + 5 ln (3)

Dezimale

9.49306 \dots

Schritte zur Lösung

\int_{1}^{3} \frac{x ^{2} + 5}{x} d x

Multipliziere aus

\frac{x ^{2} + 5}{x} : x + \frac{5}{x}

= \int_{1}^{3} x + \frac{5}{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}^{3} x d x + \int_{1}^{3} \frac{5}{x} d x

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

\int_{1}^{3} \frac{5}{x} d x = 5 ln (3)

= 4 + 5 ln (3)

\int_{- 5}^{5} ∣ x + 3 ∣ d x

\int_{- 10}^{8} 80 - 2 x - x^{2} d x

\int_{8}^{12} ln (\frac{x}{2} - 3) d x

\int_{\frac{π}{3}}^{\frac{π}{2}} \frac{1}{sin ( x )} d x

\int_{0}^{0.5} 2 x + 3 - x e^{3 x} d x