積分記号 (1/x)(cos(x)-sin(x))

解

積分記号

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

Ci (x) - Si (x) + C

解答ステップ

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

簡素化

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

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

拡張

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

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

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

\int \frac{sin ( x )}{x} d x = Si (x)

= Ci (x) - Si (x)

定数を解答に追加する

= Ci (x) - Si (x) + C