integral of 3x^4-17+1/x-sin(x)

解答

\int 3 x^{4} - 17 + \frac{1}{x} - sin (x) d x

\frac{3 x ^{5}}{5} - 17 x + ln ∣ x ∣ + cos (x) + C

求解步骤

\int 3 x^{4} - 17 + \frac{1}{x} - sin (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 x^{4} d x - \int 17 d x + \int \frac{1}{x} d x - \int sin (x) d x

\int 3 x^{4} d x = \frac{3 x ^{5}}{5}

\int 17 d x = 17 x

\int \frac{1}{x} d x = ln ∣ x ∣

\int sin (x) d x = - cos (x)

= \frac{3 x ^{5}}{5} - 17 x + ln ∣ x ∣ - (- cos (x))

化简

= \frac{3 x ^{5}}{5} - 17 x + ln ∣ x ∣ + cos (x)

解答补常数

= \frac{3 x ^{5}}{5} - 17 x + ln ∣ x ∣ + cos (x) + C

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