integral of ((4x^4+3x^3-2x)/x)

解答

\int (\frac{4 x ^{4} + 3 x ^{3} - 2 x}{x}) d x

x^{4} + x^{3} - 2 x + C

求解步骤

\int \frac{4 x ^{4} + 3 x ^{3} - 2 x}{x} d x

乘开

\frac{4 x ^{4} + 3 x ^{3} - 2 x}{x} : \frac{4 x ^{4}}{x} + \frac{3 x ^{3}}{x} - \frac{2 x}{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 \frac{4 x ^{4}}{x} d x + \int \frac{3 x ^{3}}{x} d x - \int \frac{2 x}{x} d x

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

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

\int \frac{2 x}{x} d x = 2 x

= x^{4} + x^{3} - 2 x

解答补常数

= x^{4} + x^{3} - 2 x + C

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