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

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

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

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

2 Si (x) + C

Solution steps

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

Apply u-substitution

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

Take the constant out:

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

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

Use the nonelementary integral:

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

= 2 Si (u)

Substitute back

u = x

= 2 Si (x)

Add a constant to the solution

= 2 Si (x) + C

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