integral of (x^3+\sqrt[3]{x})

解答

\int (x^{3} + 3 x) d x

\frac{x ^{4}}{4} + \frac{3}{4} x^{\frac{4}{3}} + C

求解步骤

\int x^{3} + 3 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 x^{3} d x + \int 3 x d x

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

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

= \frac{x ^{4}}{4} + \frac{3}{4} x^{\frac{4}{3}}

解答补常数

= \frac{x ^{4}}{4} + \frac{3}{4} x^{\frac{4}{3}} + C

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