The discussion centers on the integration of the function dx/(x ln(x)^4). The correct approach involves using the substitution u = ln(x), leading to the integral transforming into (1/4)ln(ln(x)) + C. Participants clarify that the expression (du)(x)/(4x u) is unnecessary, as substituting du for dx/x simplifies the process. The final result confirms the integration technique and highlights the importance of proper substitution in calculus.
PREREQUISITESStudents studying calculus, particularly those focusing on integration techniques, as well as educators seeking to clarify substitution methods in mathematical discussions.
You mean the integral of this don't you?ArmiAldi said:let me know is this correct or no?
dx)/(x lnx^4)
Well, (1/4) ln(ln(x))+ C. And you didn't really need to write "(du)(x)/(4x u)". From du/dx= 1/x, du= dx/x and you can go ahead and substitute du for the dx/x you already have in the integral.(dx)/(x 4lnx)
(dx)/(4x lnx)
u = lnx
du/dx = 1/x
(du)(x) = dx
lnx = u dx = (du)(x)
(du)(x)/(4x u)
du/4u
(1/4)ln(u)
(1/4)ln(lnx)