integral of x^{-2}sin(x)

解

\int x^{- 2} sin (x) d x

- \frac{sin ( x )}{x} + Ci (x) + C

解答ステップ

\int x^{- 2} sin (x) d x

簡素化

x^{- 2} sin (x) : \frac{sin ( x )}{x ^{2}}

= \int \frac{sin ( x )}{x ^{2}} d x

部分積分を適用する

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

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

= - \frac{sin ( x )}{x} - (- Ci (x))

簡素化

= - \frac{sin ( x )}{x} + Ci (x)

定数を解答に追加する

= - \frac{sin ( x )}{x} + Ci (x) + C