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

The integral of (sin(sqrt(y*x)))/y is 2\Si(sqrt(xy))+C

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integral of (sin(sqrt(y*x)))/y

\int \frac{sin ( y \cdot x )}{y} d y

2 Si (x y) + C

Solution steps

\int \frac{sin ( y x )}{y} d y

Apply u-substitution

: \int \frac{sin ( u )}{u} d u

= \int \frac{sin ( u )}{u} d u

Apply u-substitution

: \int \frac{2 sin ( v )}{v} d v

= \int \frac{2 sin ( v )}{v} d v

Take the constant out:

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

= 2 \cdot \int \frac{sin ( v )}{v} d v

Use the nonelementary integral:

\int \frac{sin ( x )}{x} d x = Si (x)

= 2 Si (v)

Substitute back

= 2 Si (x y)

Add a constant to the solution

= 2 Si (x y) + C

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What is the integral of (sin(sqrt(y*x)))/y ?
The integral of (sin(sqrt(y*x)))/y is 2\Si(sqrt(xy))+C