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

解

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

\frac{6 x ^{7}}{7} + \frac{x ^{6}}{2} + \frac{5 x ^{2}}{2} - 4 x + C

解答ステップ

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

\int 6 x^{6} d x = \frac{6 x ^{7}}{7}

\int 3 x^{5} d x = \frac{x ^{6}}{2}

\int 5 x d x = \frac{5 x ^{2}}{2}

\int 4 d x = 4 x

= \frac{6 x ^{7}}{7} + \frac{x ^{6}}{2} + \frac{5 x ^{2}}{2} - 4 x

定数を解答に追加する

= \frac{6 x ^{7}}{7} + \frac{x ^{6}}{2} + \frac{5 x ^{2}}{2} - 4 x + C