What is the integral of (sin(2sqrt(x)))/(sqrt(x)) ?

The integral of (sin(2sqrt(x)))/(sqrt(x)) is -cos(2sqrt(x))+C

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integral of (sin(2sqrt(x)))/(sqrt(x))

\int \frac{sin ( 2 x )}{x} d x

- cos (2 x) + C

Solution steps

\int \frac{sin ( 2 x )}{x} d x

Apply u-substitution

: \int sin (u) d u

= \int sin (u) d u

Use the common integral:

\int sin (u) d u = - cos (u)

= - cos (u)

Substitute back

u = 2 x

= - cos (2 x)

Add a constant to the solution

= - cos (2 x) + C

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