What is the integral of (8/(sqrt(x))+8sqrt(x)) ?

The integral of (8/(sqrt(x))+8sqrt(x)) is 16sqrt(x)+16/3 x^{3/2}+C

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integral of (8/(sqrt(x))+8sqrt(x))

\int (\frac{8}{x} + 8 x) d x

16 x + \frac{16}{3} x^{\frac{3}{2}} + C

Solution steps

\int \frac{8}{x} + 8 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{8}{x} d x + \int 8 x d x

\int \frac{8}{x} d x = 16 x

\int 8 x d x = \frac{16}{3} x^{\frac{3}{2}}

= 16 x + \frac{16}{3} x^{\frac{3}{2}}

Add a constant to the solution

= 16 x + \frac{16}{3} x^{\frac{3}{2}} + C

\frac{d}{d x} (x sec (x) tan (x))

f (x) = x + \frac{9}{x}

\frac{\partial}{\partial x} ((x y)^{z})

\int \frac{x ^{3} - x ^{2} - 4 x + 4}{x ^{3} - x ^{2} - 6 x} d x

\frac{\partial}{\partial x} (e^{2 y} cos (3 x))

What is the integral of (8/(sqrt(x))+8sqrt(x)) ?
The integral of (8/(sqrt(x))+8sqrt(x)) is 16sqrt(x)+16/3 x^{3/2}+C