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

The integral of (2sin(sqrt(x)))/(sqrt(x)) is -4cos(sqrt(x))+C

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

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

- 4 cos (x) + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int 2 sin (u) d u

= 2 \cdot \int 2 sin (u) d u

Take the constant out:

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

= 2 \cdot 2 \cdot \int sin (u) d u

Use the common integral:

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

= 2 \cdot 2 (- cos (u))

Substitute back

u = x

= 2 \cdot 2 (- cos (x))

Simplify

= - 4 cos (x)

Add a constant to the solution

= - 4 cos (x) + C

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What is the integral of (2sin(sqrt(x)))/(sqrt(x)) ?
The integral of (2sin(sqrt(x)))/(sqrt(x)) is -4cos(sqrt(x))+C