integral of (u+u^4)

解答

\int (u + u^{4}) d u

\frac{u ^{2}}{2} + \frac{u ^{5}}{5} + C

求解步骤

\int u + u^{4} d u

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 u d u + \int u^{4} d u

\int u d u = \frac{u ^{2}}{2}

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

= \frac{u ^{2}}{2} + \frac{u ^{5}}{5}

解答补常数

= \frac{u ^{2}}{2} + \frac{u ^{5}}{5} + C

\int_{1}^{1000} \frac{33}{x ^{3}} d x

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