What is the integral of 3/(sqrt(x))+sin(2x) ?

The integral of 3/(sqrt(x))+sin(2x) is 6sqrt(x)-1/2 cos(2x)+C

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integral of 3/(sqrt(x))+sin(2x)

\int \frac{3}{x} + sin (2 x) d x

6 x - \frac{1}{2} cos (2 x) + C

Solution steps

\int \frac{3}{x} + sin (2 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 \frac{3}{x} d x + \int sin (2 x) d x

\int \frac{3}{x} d x = 6 x

\int sin (2 x) d x = - \frac{1}{2} cos (2 x)

= 6 x - \frac{1}{2} cos (2 x)

Add a constant to the solution

= 6 x - \frac{1}{2} cos (2 x) + C

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What is the integral of 3/(sqrt(x))+sin(2x) ?
The integral of 3/(sqrt(x))+sin(2x) is 6sqrt(x)-1/2 cos(2x)+C