integral of (4cosh(x)+x^5)

解

\int (4 cosh (x) + x^{5}) d x

4 sinh (x) + \frac{x ^{6}}{6} + C

解答ステップ

\int 4 cosh (x) + x^{5} 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 4 cosh (x) d x + \int x^{5} d x

\int 4 cosh (x) d x = 4 sinh (x)

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

= 4 sinh (x) + \frac{x ^{6}}{6}

定数を解答に追加する

= 4 sinh (x) + \frac{x ^{6}}{6} + C