What is the integral of ((10)/(sqrt(x))+10sqrt(x)) ?

The integral of ((10)/(sqrt(x))+10sqrt(x)) is 20sqrt(x)+20/3 x^{3/2}+C

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integral of ((10)/(sqrt(x))+10sqrt(x))

\int (\frac{10}{x} + 10 x) d x

20 x + \frac{20}{3} x^{\frac{3}{2}} + C

Solution steps

\int \frac{10}{x} + 10 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{10}{x} d x + \int 10 x d x

\int \frac{10}{x} d x = 20 x

\int 10 x d x = \frac{20}{3} x^{\frac{3}{2}}

= 20 x + \frac{20}{3} x^{\frac{3}{2}}

Add a constant to the solution

= 20 x + \frac{20}{3} x^{\frac{3}{2}} + C

x \to 0 lim (\frac{x ( x )}{x + x})

f (x) = (3 x + 7)^{2}

\frac{d}{d x} f (x) = (5 x - 5 x^{3}) (7 + x)

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

What is the integral of ((10)/(sqrt(x))+10sqrt(x)) ?
The integral of ((10)/(sqrt(x))+10sqrt(x)) is 20sqrt(x)+20/3 x^{3/2}+C