integral of y^2cos(x)-sin(x)

解

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

cos (x) + y^{2} sin (x) + C

解答ステップ

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

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

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

= - (- cos (x)) + y^{2} sin (x)

簡素化

= cos (x) + y^{2} sin (x)

定数を解答に追加する

= cos (x) + y^{2} sin (x) + C