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

The integral of sqrt(y/x) is 2sqrt(y)sqrt(x)+C

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integral of sqrt(y/x)

\int \frac{y}{x} d x

2 y x + C

Solution steps

\int \frac{y}{x} d x

Apply u-substitution

: \int - \frac{y}{u ^{\frac{3}{2}}} d u

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

Take the constant out:

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

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

Apply the Power Rule

: - \frac{2}{u}

= - y (- \frac{2}{u})

Substitute back

u = \frac{y}{x}

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

Simplify

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

= 2 y x

Add a constant to the solution

= 2 y x + C

n = 2 \sum \infty \frac{n}{( n - 1 ) !}

\int_{0}^{1} cos (x^{3}) d x

\int - 5 sin (5 x) d x

f (y) = 4 y^{2}

\frac{d}{d x} (x lo g_{2} (x - 3))

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