What is the integral of ((sqrt(y))/5+2/(sqrt(y))) ?

The integral of ((sqrt(y))/5+2/(sqrt(y))) is 2/15 y^{3/2}+4sqrt(y)+C

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integral of ((sqrt(y))/5+2/(sqrt(y)))

\int (\frac{y}{5} + \frac{2}{y}) d y

\frac{2}{15} y^{\frac{3}{2}} + 4 y + C

Solution steps

\int \frac{y}{5} + \frac{2}{y} 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{y}{5} d y + \int \frac{2}{y} d y

\int \frac{y}{5} d y = \frac{2}{15} y^{\frac{3}{2}}

\int \frac{2}{y} d y = 4 y

= \frac{2}{15} y^{\frac{3}{2}} + 4 y

Add a constant to the solution

= \frac{2}{15} y^{\frac{3}{2}} + 4 y + C

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What is the integral of ((sqrt(y))/5+2/(sqrt(y))) ?
The integral of ((sqrt(y))/5+2/(sqrt(y))) is 2/15 y^{3/2}+4sqrt(y)+C