integral of (6x^2+8x-sin(x))

解

\int (6 x^{2} + 8 x - sin (x)) d x

2 x^{3} + 4 x^{2} + cos (x) + C

解答ステップ

\int 6 x^{2} + 8 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 6 x^{2} d x + \int 8 x d x - \int sin (x) d x

\int 6 x^{2} d x = 2 x^{3}

\int 8 x d x = 4 x^{2}

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

= 2 x^{3} + 4 x^{2} - (- cos (x))

簡素化

= 2 x^{3} + 4 x^{2} + cos (x)

定数を解答に追加する

= 2 x^{3} + 4 x^{2} + cos (x) + C