What is the integral of (4y)/(sqrt(x^3)) ?

The integral of (4y)/(sqrt(x^3)) is -(8y)/(sqrt(x))+C

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integral of (4y)/(sqrt(x^3))

\int \frac{4 y}{x ^{3}} d x

- \frac{8 y}{x} + C

Solution steps

\int \frac{4 y}{x ^{3}} d x

Take the constant out:

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

= 4 y \cdot \int \frac{1}{x ^{3}} d x

Apply exponent rule:

(a^{n})^{m} = a^{n \cdot m}

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

= 4 y \cdot \int \frac{1}{x ^{\frac{3}{2}}} d x

Apply the Power Rule

: - \frac{2}{x}

= 4 y (- \frac{2}{x})

Simplify

4 y (- \frac{2}{x}) : - \frac{8 y}{x}

= - \frac{8 y}{x}

Add a constant to the solution

= - \frac{8 y}{x} + C

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What is the integral of (4y)/(sqrt(x^3)) ?
The integral of (4y)/(sqrt(x^3)) is -(8y)/(sqrt(x))+C