integral of 4sinh(x)+x^7

解答

\int 4 sinh (x) + x^{7} d x

4 cosh (x) + \frac{x ^{8}}{8} + C

求解步骤

\int 4 sinh (x) + x^{7} d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 4 sinh (x) d x + \int x^{7} d x

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

\int x^{7} d x = \frac{x ^{8}}{8}

= 4 cosh (x) + \frac{x ^{8}}{8}

解答补常数

= 4 cosh (x) + \frac{x ^{8}}{8} + C

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