integral of (sin(2x))/(x^2)

解

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

- \frac{sin ( 2 x )}{x} + 2 Ci (2 x) + C

解答ステップ

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

部分積分を適用する

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

\int - \frac{2 cos ( 2 x )}{x} d x = - 2 Ci (2 x)

= - \frac{sin ( 2 x )}{x} - (- 2 Ci (2 x))

簡素化

= - \frac{sin ( 2 x )}{x} + 2 Ci (2 x)

定数を解答に追加する

= - \frac{sin ( 2 x )}{x} + 2 Ci (2 x) + C