What is the integral of (4+6x)/(sqrt(x)) ?

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

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integral of (4+6x)/(sqrt(x))

\int \frac{4 + 6 x}{x} d x

2 x (4 + 6 x) - 8 x^{\frac{3}{2}} + C

Solution steps

\int \frac{4 + 6 x}{x} d x

Apply Integration By Parts

: 2 x (4 + 6 x) - \int 12 x d x

= 2 x (4 + 6 x) - \int 12 x d x

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

= 2 x (4 + 6 x) - 8 x^{\frac{3}{2}}

Add a constant to the solution

= 2 x (4 + 6 x) - 8 x^{\frac{3}{2}} + C

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