integral of 3sec(2)(x)+2x-8x

解

\int 3 sec (2) (x) + 2 x - 8 x d x

\frac{3}{2} sec (2) x^{2} - 3 x^{2} + C

解答ステップ

\int 3 sec (2) x + 2 x - 8 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 3 sec (2) x d x + \int 2 x d x - \int 8 x d x

\int 3 sec (2) x d x = \frac{3}{2} sec (2) x^{2}

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

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

= \frac{3}{2} sec (2) x^{2} + x^{2} - 4 x^{2}

簡素化

= \frac{3}{2} sec (2) x^{2} - 3 x^{2}

定数を解答に追加する

= \frac{3}{2} sec (2) x^{2} - 3 x^{2} + C