integral of (e^{9x}-9/x)

解答

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

\frac{1}{9} e^{9 x} - 9 ln ∣ x ∣ + C

求解步骤

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

\int e^{9 x} d x = \frac{1}{9} e^{9 x}

\int \frac{9}{x} d x = 9 ln ∣ x ∣

= \frac{1}{9} e^{9 x} - 9 ln ∣ x ∣

解答补常数

= \frac{1}{9} e^{9 x} - 9 ln ∣ x ∣ + C

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