integral of (21x^6+x-2e+3csc^2(x))

解

\int (21 x^{6} + x - 2 e + 3 csc^{2} (x)) d x

3 x^{7} + \frac{x ^{2}}{2} - 2 e x - 3 cot (x) + C

解答ステップ

\int 21 x^{6} + x - 2 e + 3 csc^{2} (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 21 x^{6} d x + \int x d x - \int 2 e d x + \int 3 csc^{2} (x) d x

\int 21 x^{6} d x = 3 x^{7}

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

\int 2 e d x = 2 e x

\int 3 csc^{2} (x) d x = - 3 cot (x)

= 3 x^{7} + \frac{x ^{2}}{2} - 2 e x - 3 cot (x)

定数を解答に追加する

= 3 x^{7} + \frac{x ^{2}}{2} - 2 e x - 3 cot (x) + C