integral of (1/(\sqrt[3]{x)}-3x^{5/2})

解答

\int (\frac{1}{3 x} - 3 x^{\frac{5}{2}}) d x

\frac{3}{2} x^{\frac{2}{3}} - \frac{6}{7} x^{\frac{7}{2}} + C

求解步骤

\int \frac{1}{3 x} - 3 x^{\frac{5}{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{1}{3 x} d x - \int 3 x^{\frac{5}{2}} d x

\int \frac{1}{3 x} d x = \frac{3}{2} x^{\frac{2}{3}}

\int 3 x^{\frac{5}{2}} d x = \frac{6}{7} x^{\frac{7}{2}}

= \frac{3}{2} x^{\frac{2}{3}} - \frac{6}{7} x^{\frac{7}{2}}

解答补常数

= \frac{3}{2} x^{\frac{2}{3}} - \frac{6}{7} x^{\frac{7}{2}} + C

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