How to Find the Indefinite Integral for (4x^2+2√x+1)/(2x√x)?

[KMcFadden]

Homework Statement

∫▒〖(4x^2+2√x+1)/(2x√x) dx〗

Homework Equations

The Attempt at a Solution

∫▒〖(4x^2+2√x+1)/(2x√x) dx〗
∫▒((4x^2)/(2x^(3/2) )+(2√x)/(2x^(3/2) )+1/(2x^(3/2) ))dx
2∫▒x^(1/2) dx+∫▒〖x^(-1) dx〗+1/2 ∫▒x^(-3/2) dx
2×2/3 x^(3/2)+ln⁡x+1/2×(-2) x^(-1/2)+C
4/3 x^(3/2)+ln⁡x-x^(-1/2)+C
4/3 √(x^3 )+ln⁡x-1/√x+C

 

[SammyS]

Homework Statement

∫▒〖(4x^2+2√x+1)/(2x√x) dx〗

Homework Equations

The Attempt at a Solution

∫▒〖(4x^2+2√x+1)/(2x√x) dx〗
∫▒((4x^2)/(2x^(3/2) )+(2√x)/(2x^(3/2) )+1/(2x^(3/2) ))dx
2∫▒x^(1/2) dx+∫▒〖x^(-1) dx〗+1/2 ∫▒x^(-3/2) dx
2×2/3 x^(3/2)+ln⁡x+1/2×(-2) x^(-1/2)+C
4/3 x^(3/2)+ln⁡x-x^(-1/2)+C
4/3 √(x^3 )+ln⁡x-1/√x+C

It looks good. Take the derivative to check it.

 

[KMcFadden]

Thanks