What is the integral of (sqrt(y)+1/(sqrt(y))) ?

The integral of (sqrt(y)+1/(sqrt(y))) is 2/3 y^{3/2}+2sqrt(y)+C

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integral of (sqrt(y)+1/(sqrt(y)))

\int (y + \frac{1}{y}) d y

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

Solution steps

\int y + \frac{1}{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 y d y + \int \frac{1}{y} d y

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

\int \frac{1}{y} d y = 2 y

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

Add a constant to the solution

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

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What is the integral of (sqrt(y)+1/(sqrt(y))) ?
The integral of (sqrt(y)+1/(sqrt(y))) is 2/3 y^{3/2}+2sqrt(y)+C