integral of (4+sqrt(x))/(x^2)

解

\int \frac{4 + x}{x ^{2}} d x

- \frac{4}{x} - \frac{2}{x} + C

解答ステップ

\int \frac{4 + x}{x ^{2}} d x

拡張

\frac{4 + x}{x ^{2}} : \frac{4}{x ^{2}} + \frac{1}{x ^{\frac{3}{2}}}

= \int \frac{4}{x ^{2}} + \frac{1}{x ^{\frac{3}{2}}} 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 \frac{4}{x ^{2}} d x + \int \frac{1}{x ^{\frac{3}{2}}} d x

\int \frac{4}{x ^{2}} d x = - \frac{4}{x}

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

= - \frac{4}{x} - \frac{2}{x}

定数を解答に追加する

= - \frac{4}{x} - \frac{2}{x} + C