integral of (5x^4+12x^3+6x-2)

解

\int (5 x^{4} + 12 x^{3} + 6 x - 2) d x

x^{5} + 3 x^{4} + 3 x^{2} - 2 x + C

解答ステップ

\int 5 x^{4} + 12 x^{3} + 6 x - 2 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 5 x^{4} d x + \int 12 x^{3} d x + \int 6 x d x - \int 2 d x

\int 5 x^{4} d x = x^{5}

\int 12 x^{3} d x = 3 x^{4}

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

\int 2 d x = 2 x

= x^{5} + 3 x^{4} + 3 x^{2} - 2 x

定数を解答に追加する

= x^{5} + 3 x^{4} + 3 x^{2} - 2 x + C