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

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

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integral of 2sqrt(y/5)

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

\frac{4}{3 5} y^{\frac{3}{2}} + C

Solution steps

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

Take the constant out:

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

= 2 \cdot \int \frac{y}{5} d y

Simplify

\frac{y}{5} : \frac{y}{5}

= 2 \cdot \int \frac{y}{5} d y

Take the constant out:

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

= 2 \cdot \frac{1}{5} \cdot \int y d y

Apply the Power Rule

: \frac{2}{3} y^{\frac{3}{2}}

= 2 \cdot \frac{1}{5} \cdot \frac{2}{3} y^{\frac{3}{2}}

Simplify

2 \cdot \frac{1}{5} \cdot \frac{2}{3} y^{\frac{3}{2}} : \frac{4}{3 5} y^{\frac{3}{2}}

= \frac{4}{3 5} y^{\frac{3}{2}}

Add a constant to the solution

= \frac{4}{3 5} y^{\frac{3}{2}} + C

\int \frac{x}{9 - x ^{4}} d x

y^{^{''}} + 2 y^{^{'}} + 5 y = 0, y (0) = 2, y^{^{'}} (0) = - 1

n \to \infty lim (\frac{1}{x ^{n - 1}})

\int_{1}^{3} x d x

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

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