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

(3, - 1), (4, 7)

y = \frac{4}{7 x ^{2}}

\frac{d y}{d x} = \frac{3 x ^{2}}{y ^{2}}

6 x^{2} + 5 x + 8, at x = 4

x \to 4 lim (x^{3} + 6 x)

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