integral of ((sqrt(y))/8+8/(sqrt(y)))

解答

\int (\frac{y}{8} + \frac{8}{y}) d y

\frac{1}{12} y^{\frac{3}{2}} + 16 y + C

求解步骤

\int \frac{y}{8} + \frac{8}{y} d y

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{y}{8} d y + \int \frac{8}{y} d y

\int \frac{y}{8} d y = \frac{1}{12} y^{\frac{3}{2}}

\int \frac{8}{y} d y = 16 y

= \frac{1}{12} y^{\frac{3}{2}} + 16 y

解答补常数

= \frac{1}{12} y^{\frac{3}{2}} + 16 y + C

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