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

解

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

sin (x) - Si (x) + C

解答ステップ

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

\int cos (x) d x = sin (x)

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

= sin (x) - Si (x)

定数を解答に追加する

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