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

(arctan (x^{2}))^{^{'}}

\int \frac{x}{( x ^{2} - 9 ) ^{2}} d x

d er i v a t i v e f (x) = \frac{5}{x ^{6}}

\int (x - 1)^{2} + 1 d x

\frac{( 1 + x ^{2} ) d y}{d x} - (1 + y^{2}) = 0

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