What is the integral of (1/7-1/(y^{5/4)}) ?

The integral of (1/7-1/(y^{5/4)}) is 1/7 y+4/(y^{1/4)}+C

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

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

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

Solution steps

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

Apply the Sum Rule:

\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}}})

Simplify

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

Add a constant to the solution

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

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What is the integral of (1/7-1/(y^{5/4)}) ?
The integral of (1/7-1/(y^{5/4)}) is 1/7 y+4/(y^{1/4)}+C