integral of (9e^x-9sqrt(x))

解答

\int (9 e^{x} - 9 x) d x

9 e^{x} - 6 x^{\frac{3}{2}} + C

求解步骤

\int 9 e^{x} - 9 x 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 9 e^{x} d x - \int 9 x d x

\int 9 e^{x} d x = 9 e^{x}

\int 9 x d x = 6 x^{\frac{3}{2}}

= 9 e^{x} - 6 x^{\frac{3}{2}}

解答补常数

= 9 e^{x} - 6 x^{\frac{3}{2}} + C

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