What is the integral of (2x+6)/(sqrt(x)) ?

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

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integral of (2x+6)/(sqrt(x))

\int \frac{2 x + 6}{x} d x

2 x (2 x + 6) - \frac{8}{3} x^{\frac{3}{2}} + C

Solution steps

\int \frac{2 x + 6}{x} d x

Apply Integration By Parts

: 2 x (2 x + 6) - \int 4 x d x

= 2 x (2 x + 6) - \int 4 x d x

\int 4 x d x = \frac{8}{3} x^{\frac{3}{2}}

= 2 x (2 x + 6) - \frac{8}{3} x^{\frac{3}{2}}

Add a constant to the solution

= 2 x (2 x + 6) - \frac{8}{3} x^{\frac{3}{2}} + C

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