What is the integral of 5/(sqrt(x))+5sqrt(x) ?

The integral of 5/(sqrt(x))+5sqrt(x) is 10sqrt(x)+10/3 x^{3/2}+C

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integral of 5/(sqrt(x))+5sqrt(x)

\int \frac{5}{x} + 5 x d x

10 x + \frac{10}{3} x^{\frac{3}{2}} + C

Solution steps

\int \frac{5}{x} + 5 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{5}{x} d x + \int 5 x d x

\int \frac{5}{x} d x = 10 x

\int 5 x d x = \frac{10}{3} x^{\frac{3}{2}}

= 10 x + \frac{10}{3} x^{\frac{3}{2}}

Add a constant to the solution

= 10 x + \frac{10}{3} x^{\frac{3}{2}} + C

\frac{d y}{d x} = 4 (x^{2} + 1)

\frac{\partial}{\partial x} (5 x + 6 y)

x \to + 3 lim (\frac{x ^{2} - 2}{3 - x})

\int sin (x + 1) d x

\int (x^{2} + 2 x) e^{3 x + 2} d x

What is the integral of 5/(sqrt(x))+5sqrt(x) ?
The integral of 5/(sqrt(x))+5sqrt(x) is 10sqrt(x)+10/3 x^{3/2}+C