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

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

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

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

- 2 cos (x + 1) + C

Solution steps

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

Apply Integration By Parts

: 2 x sin (x + 1) - \int cos (x + 1) d x

= 2 x sin (x + 1) - \int cos (x + 1) d x

\int cos (x + 1) d x = 2 (x sin (x + 1) + cos (x + 1))

= 2 x sin (x + 1) - 2 (x sin (x + 1) + cos (x + 1))

Simplify

2 x sin (x + 1) - 2 (x sin (x + 1) + cos (x + 1)) : - 2 cos (x + 1)

= - 2 cos (x + 1)

Add a constant to the solution

= - 2 cos (x + 1) + C

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