What is the integral of 2x+4/(sqrt(x)) ?

The integral of 2x+4/(sqrt(x)) is x^2+8sqrt(x)+C

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integral of 2x+4/(sqrt(x))

\int 2 x + \frac{4}{x} d x

x^{2} + 8 x + C

Solution steps

\int 2 x + \frac{4}{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 2 x d x + \int \frac{4}{x} d x

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

\int \frac{4}{x} d x = 8 x

= x^{2} + 8 x

Add a constant to the solution

= x^{2} + 8 x + C

What is the integral of 2x+4/(sqrt(x)) ?
The integral of 2x+4/(sqrt(x)) is x^2+8sqrt(x)+C