integral of (5x-(x^3)/2+(ARyx^2)/2+C)

解答

\int (5 x - \frac{x ^{3}}{2} + \frac{A R y x ^{2}}{2} + C) d x

\frac{A R y x ^{3}}{6} - \frac{x ^{4}}{8} + C x + \frac{5 x ^{2}}{2} + C

求解步骤

\int 5 x - \frac{x ^{3}}{2} + \frac{A R y x ^{2}}{2} + C 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 \frac{A R y x ^{2}}{2} d x - \int \frac{x ^{3}}{2} d x + \int C d x + \int 5 x d x

\int \frac{A R y x ^{2}}{2} d x = \frac{A R y x ^{3}}{6}

\int \frac{x ^{3}}{2} d x = \frac{x ^{4}}{8}

\int C d x = C x

\int 5 x d x = \frac{5 x ^{2}}{2}

= \frac{A R y x ^{3}}{6} - \frac{x ^{4}}{8} + C x + \frac{5 x ^{2}}{2}

解答补常数

= \frac{A R y x ^{3}}{6} - \frac{x ^{4}}{8} + C x + \frac{5 x ^{2}}{2} + C

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