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

y = - \frac{e ^{- x}}{2} cos (2 x)

f (x) = x^{3} - 4 x^{2} - 1

\frac{d y}{d t} = - \frac{y}{t} - 8

\frac{d}{d x} (e^{4 x} 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