What is the integral of ((12)/(sqrt(x))+12sqrt(x)) ?

The integral of ((12)/(sqrt(x))+12sqrt(x)) is 24sqrt(x)+8x^{3/2}+C

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integral of ((12)/(sqrt(x))+12sqrt(x))

\int (\frac{12}{x} + 12 x) d x

24 x + 8 x^{\frac{3}{2}} + C

Solution steps

\int \frac{12}{x} + 12 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{12}{x} d x + \int 12 x d x

\int \frac{12}{x} d x = 24 x

\int 12 x d x = 8 x^{\frac{3}{2}}

= 24 x + 8 x^{\frac{3}{2}}

Add a constant to the solution

= 24 x + 8 x^{\frac{3}{2}} + C

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What is the integral of ((12)/(sqrt(x))+12sqrt(x)) ?
The integral of ((12)/(sqrt(x))+12sqrt(x)) is 24sqrt(x)+8x^{3/2}+C