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

f (x) = x^{7} + x^{5} + x^{3} + x + 1

(3.3) (4.5)

\int_{0}^{\frac{π}{3}} cos^{3} (3 x) d x

\int \frac{cos ( x )}{sin ^{2} ( x ) - 4} d x

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

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