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

The integral of 4/(sqrt(x))+4sqrt(x) is 8sqrt(x)+8/3 x^{3/2}+C

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

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

8 x + \frac{8}{3} x^{\frac{3}{2}} + C

Solution steps

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

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

\int 4 x d x = \frac{8}{3} x^{\frac{3}{2}}

= 8 x + \frac{8}{3} x^{\frac{3}{2}}

Add a constant to the solution

= 8 x + \frac{8}{3} x^{\frac{3}{2}} + C

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

e^{x} y y^{^{'}} = e^{- y} + e^{- 2 x - y}

\frac{d}{d x} (5 sin (4 x))

(2 x)^{x}

\int \frac{2}{16 + 3 x ^{2}} d x

What is the integral of 4/(sqrt(x))+4sqrt(x) ?
The integral of 4/(sqrt(x))+4sqrt(x) is 8sqrt(x)+8/3 x^{3/2}+C