What is the integral of (cos(sqrt(x)))/x ?

The integral of (cos(sqrt(x)))/x is 2\Ci(sqrt(x))+C

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integral of (cos(sqrt(x)))/x

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

2 Ci (x) + C

Solution steps

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

Apply u-substitution

: \int \frac{2 cos ( u )}{u} d u

= \int \frac{2 cos ( u )}{u} d u

Take the constant out:

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

= 2 \cdot \int \frac{cos ( u )}{u} d u

Use the nonelementary integral:

\int \frac{cos ( x )}{x} d x = Ci (x)

= 2 Ci (u)

Substitute back

u = x

= 2 Ci (x)

Add a constant to the solution

= 2 Ci (x) + C

f (x) = 5 (7 + x)

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

x \to 1 - lim (x)

\int 2 x^{9} e^{- x^{5}} d x

\int \frac{9}{x ^{2} x ^{2} + 4} d x

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