1. integral (3+2x^2)/xdx

how would one solve this?
I used integration by parts and got

(3+2x^2)lnx - 1/2x^2lnx - 1/4x^2

it's a differential equation os

1/3y^3 = (3+2x^2)lnx - 1/2x^2lnx - 1/4x^2 where y(1) = 0

2. Originally Posted by khuezy
how would one solve this?
I used integration by parts and got

(3+2x^2)lnx - 1/2x^2lnx - 1/4x^2

it's a differential equation os

1/3y^3 = (3+2x^2)lnx - 1/2x^2lnx - 1/4x^2 where y(1) = 0
By parts is not required, you can do it this way...
$\int \frac{3+2x^2}{x} \, dx = \int \left(\frac{3}{x}+2x\right)\, dx = 3\ln x + x^2 +C$

3. Originally Posted by Isomorphism
By parts is not required, you can do it this way...
$\int \frac{3+2x^2}{x} \, dx = \int \left(\frac{3}{x}+2x\right)\, dx = 3\ln x + x^2 +C$
*Ahem* $3\ln {\color{red}|}x{\color{red}|} + x^2 +C$