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

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

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

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

- 2 cos (x) + C

Solution steps

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

Apply u-substitution

: \int 2 sin (u) d u

= \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 \int sin (u) d u

Use the common integral:

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

= 2 (- cos (u))

Substitute back

u = x

= 2 (- cos (x))

Simplify

= - 2 cos (x)

Add a constant to the solution

= - 2 cos (x) + C

\frac{d}{d x} (3 + 4.1 cos (0.9 x))

\frac{d y}{d x} + x y = 4 x

\frac{\partial}{\partial y} (25 - x^{2} - y^{2})

\frac{d}{d x} (arctan (8 x))

y = (9 x)^{3 x}

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