integral of x^{sqrt(2)}-3/(sqrt(x))+5/x

解

\int x^{2} - \frac{3}{x} + \frac{5}{x} d x

(2 - 1) x^{2 + 1} - 6 x + 5 ln ∣ x ∣ + C

解答ステップ

\int x^{2} - \frac{3}{x} + \frac{5}{x} d x

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x^{2} d x - \int \frac{3}{x} d x + \int \frac{5}{x} d x

\int x^{2} d x = (2 - 1) x^{2 + 1}

\int \frac{3}{x} d x = 6 x

\int \frac{5}{x} d x = 5 ln ∣ x ∣

= (2 - 1) x^{2 + 1} - 6 x + 5 ln ∣ x ∣

定数を解答に追加する

= (2 - 1) x^{2 + 1} - 6 x + 5 ln ∣ x ∣ + C