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

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

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

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

\frac{x ^{2}}{2} - 2 cos (x) + C

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int x d x = \frac{x ^{2}}{2}

\int \frac{sin ( x )}{x} d x = - 2 cos (x)

= \frac{x ^{2}}{2} - 2 cos (x)

Add a constant to the solution

= \frac{x ^{2}}{2} - 2 cos (x) + C

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