integral of (1/7-1/(y^{5/4)})

解答

\int (\frac{1}{7} - \frac{1}{y ^{\frac{5}{4}}}) d y

\frac{1}{7} y + \frac{4}{y ^{\frac{1}{4}}} + C

求解步骤

\int \frac{1}{7} - \frac{1}{y ^{\frac{5}{4}}} 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{1}{7} d y - \int \frac{1}{y ^{\frac{5}{4}}} d y

\int \frac{1}{7} d y = \frac{1}{7} y

\int \frac{1}{y ^{\frac{5}{4}}} d y = - \frac{4}{y ^{\frac{1}{4}}}

= \frac{1}{7} y - (- \frac{4}{y ^{\frac{1}{4}}})

化简

= \frac{1}{7} y + \frac{4}{y ^{\frac{1}{4}}}

解答补常数

= \frac{1}{7} y + \frac{4}{y ^{\frac{1}{4}}} + C

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