What is the integral of (y^{3/2})/(2sqrt(x)) ?

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

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integral of (y^{3/2})/(2sqrt(x))

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

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{y ^{\frac{3}{2}}}{2} \cdot \int \frac{1}{x} d x

Apply the Power Rule

: 2 x^{\frac{1}{2}}

= \frac{y ^{\frac{3}{2}}}{2} \cdot 2 x^{\frac{1}{2}}

Simplify

\frac{y ^{\frac{3}{2}}}{2} \cdot 2 x^{\frac{1}{2}} : y^{\frac{3}{2}} x

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

Add a constant to the solution

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

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