integral of (x^2)/2-x^4+1205/2

解答

\int \frac{x ^{2}}{2} - x^{4} + \frac{1205}{2} d x

\frac{x ^{3}}{6} - \frac{x ^{5}}{5} + \frac{1205}{2} x + C

求解步骤

\int \frac{x ^{2}}{2} - x^{4} + \frac{1205}{2} 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{x ^{2}}{2} d x - \int x^{4} d x + \int \frac{1205}{2} d x

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

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

\int \frac{1205}{2} d x = \frac{1205}{2} x

= \frac{x ^{3}}{6} - \frac{x ^{5}}{5} + \frac{1205}{2} x

解答补常数

= \frac{x ^{3}}{6} - \frac{x ^{5}}{5} + \frac{1205}{2} x + C

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