What is the integral of (3x+2)/(sqrt(x)) ?

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

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integral of (3x+2)/(sqrt(x))

\int \frac{3 x + 2}{x} d x

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

Solution steps

\int \frac{3 x + 2}{x} d x

Apply Integration By Parts

: 2 x (3 x + 2) - \int 6 x d x

= 2 x (3 x + 2) - \int 6 x d x

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

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

Add a constant to the solution

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

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