integral of (sinh(x)+x^2)

解

\int (sinh (x) + x^{2}) d x

cosh (x) + \frac{x ^{3}}{3} + C

解答ステップ

\int sinh (x) + 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 sinh (x) d x + \int x^{2} d x

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

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

= cosh (x) + \frac{x ^{3}}{3}

定数を解答に追加する

= cosh (x) + \frac{x ^{3}}{3} + C