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`int x(3+2/x)^2 dx` Find the indefinite integral

`intx(3+2/x)^2dx`


Let's simplify the numerator of the integral ,


`x(3+2/x)^2=x{3^2+2(3)(2/x)+(2/x)^2}`


`=x{9+12/x+4/x^2}`


`=9x+12+4/x`


Now,`intx(3+2/x)^2dx=int(9x+12+4/x)dx`


Apply the sum rule and take the constant's out,


`=int9xdx+int12dx+int4/xdx`


`=9intxdx+12intdx+4int1/xdx`


Apply the power rule and use the common integral `int1/xdx=ln|x|`


`=9(x^(1+1)/(1+1))+12x+4ln|x|`


simplify and add a constant C to the solution,


`=(9x^2)/2+12x+4ln|x|+C`

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