integral of ((cos(x)-1))/x

解

\int \frac{( cos ( x ) - 1 )}{x} d x

Ci (x) - ln ∣ x ∣ + C

解答ステップ

\int \frac{cos ( x ) - 1}{x} d x

拡張

\frac{cos ( x ) - 1}{x} : \frac{cos ( x )}{x} - \frac{1}{x}

= \int \frac{cos ( x )}{x} - \frac{1}{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 \frac{cos ( x )}{x} d x - \int \frac{1}{x} d x

\int \frac{cos ( x )}{x} d x = Ci (x)

\int \frac{1}{x} d x = ln ∣ x ∣

= Ci (x) - ln ∣ x ∣

定数を解答に追加する

= Ci (x) - ln ∣ x ∣ + C