integral of \sqrt[6]{2}+\sqrt[6]{x}

解答

\int 62 + 6 x d x

62 x + \frac{6}{7} x^{\frac{7}{6}} + C

求解步骤

\int 62 + 6 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 62 d x + \int 6 x d x

\int 62 d x = 62 x

\int 6 x d x = \frac{6}{7} x^{\frac{7}{6}}

= 62 x + \frac{6}{7} x^{\frac{7}{6}}

解答补常数

= 62 x + \frac{6}{7} x^{\frac{7}{6}} + C

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