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Popular >

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

Solution

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

Solution

- \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

Popular Examples

integral of 1/((x+1)^2sqrt(x^2+2x+2))

\int \frac{1}{( x + 1 ) ^{2} x ^{2} + 2 x + 2} d x

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\int 9 x (4 + 3 x)^{5} d x

integral of (3y^2)/(x-5)

\int \frac{3 y ^{2}}{x - 5} d x

integral of 0.1682x^2+0.0987x+0.4774

\int 0.1682 x^{2} + 0.0987 x + 0.4774 d x

integral of x(3x^3-2)

\int x (3 x^{3} - 2) d x

Frequently Asked Questions (FAQ)

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