integral of x^3+1/x-7

解答

\int x^{3} + \frac{1}{x} - 7 d x

\frac{x ^{4}}{4} + ln ∣ x ∣ - 7 x + C

求解步骤

\int x^{3} + \frac{1}{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 x^{3} d x + \int \frac{1}{x} d x - \int 7 d x

\int x^{3} d x = \frac{x ^{4}}{4}

\int \frac{1}{x} d x = ln ∣ x ∣

\int 7 d x = 7 x

= \frac{x ^{4}}{4} + ln ∣ x ∣ - 7 x

解答补常数

= \frac{x ^{4}}{4} + ln ∣ x ∣ - 7 x + C

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