What is the integral of (cos(sqrt(x)+1))/(sqrt(x)) ?

The integral of (cos(sqrt(x)+1))/(sqrt(x)) is 2sin(sqrt(x)+1)+C

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integral of (cos(sqrt(x)+1))/(sqrt(x))

\int \frac{cos ( x + 1 )}{x} d x

2 sin (x + 1) + C

Solution steps

\int \frac{cos ( x + 1 )}{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 + 1

= 2 sin (x + 1)

Add a constant to the solution

= 2 sin (x + 1) + C

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What is the integral of (cos(sqrt(x)+1))/(sqrt(x)) ?
The integral of (cos(sqrt(x)+1))/(sqrt(x)) is 2sin(sqrt(x)+1)+C