integral of (3e^x+4/x)

解答

\int (3 e^{x} + \frac{4}{x}) d x

3 e^{x} + 4 ln ∣ x ∣ + C

求解步骤

\int 3 e^{x} + \frac{4}{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 3 e^{x} d x + \int \frac{4}{x} d x

\int 3 e^{x} d x = 3 e^{x}

\int \frac{4}{x} d x = 4 ln ∣ x ∣

= 3 e^{x} + 4 ln ∣ x ∣

解答补常数

= 3 e^{x} + 4 ln ∣ x ∣ + C

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