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

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

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

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

2 sin (x) + C

Solution steps

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

Apply u-substitution

: \int 2 cos (u) d u

= \int 2 cos (u) d u

Take the constant out:

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

= 2 \cdot \int cos (u) d u

Use the common integral:

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

= 2 sin (u)

Substitute back

u = x

= 2 sin (x)

Add a constant to the solution

= 2 sin (x) + C

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\int_{0}^{1} (6 x^{e} + 5 e^{x}) d x

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