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

\int_{6}^{8} \frac{90}{( x - 6 ) ^{3}} d x

\frac{d}{d x} ((x^{2} - 1) (x^{2} - 10 x + \frac{2}{x ^{2}}))

\int (ln (x))^{5} d x

t^{3} \frac{d y}{d t} + 3 t^{2} y = 8 cos (t), y (π) = 0

y = (x^{2} - 2 x + 2) e^{\frac{5 x}{2}}

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