Question

integral dx/(x((x^2)+2))

Answer 1

good question. that's your answer.

Answer 2

∫dx/x(x² + 2)
Let (x² +2) = z
differentiate,
  2x.dx = dz use this above ,
 
∫1/2dz/(z -2).z 
⇒1/2.∫dz{1/z - 1/(z - 2)}(-1/2)
⇒-1/4.[∫dz/z -dz/(z-2)]
⇒-1/4[㏑z - ㏑(z-2)]
⇒1/4.㏑(z-2)/z
⇒1/4㏑x²/(x²+2)