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

2 x y^{^{'}} - 10 y = x^{- 2}

n \to \infty lim (n (n + 1))

\int (\frac{cy}{( x ^{2} + y ^{2} ) ^{\frac{3}{2}}}) d y

\int sin (4 x) d x

z \to 2 i lim (\frac{z ^{2}}{2})

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