What is the integral of 8/x+6sqrt(x) ?

The integral of 8/x+6sqrt(x) is 8ln|x|+4x^{3/2}+C

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integral of 8/x+6sqrt(x)

\int \frac{8}{x} + 6 x d x

8 ln ∣ x ∣ + 4 x^{\frac{3}{2}} + C

Solution steps

\int \frac{8}{x} + 6 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 6 x d x

\int \frac{8}{x} d x = 8 ln ∣ x ∣

\int 6 x d x = 4 x^{\frac{3}{2}}

= 8 ln ∣ x ∣ + 4 x^{\frac{3}{2}}

Add a constant to the solution

= 8 ln ∣ x ∣ + 4 x^{\frac{3}{2}} + C

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What is the integral of 8/x+6sqrt(x) ?
The integral of 8/x+6sqrt(x) is 8ln|x|+4x^{3/2}+C