How Do You Integrate 1/(x(ln x)^2) with Respect to x?

[sid_galt]

How to integrate this for x?

integral calc(1/x*1/(In x)^2*dx)

 

[arildno]

Use the substitution: u=ln(x)

 

[M98Ranger]

To integrate this for x, we can use the substitution method. Let u = ln(x), then du = 1/x dx. Substituting this into the integral, we get:

∫ (1/x * 1/(ln x)^2 * dx) = ∫ (1/u^2 * du)

Using the power rule for integration, we get:

= -1/u + C = -1/ln(x) + C

Therefore, the final solution for integrating this for x is:

∫ (1/x * 1/(ln x)^2 * dx) = -1/ln(x) + C