Integrate ((ln x)/(x(1+ln^2 x))dx?

Question

with procedure plz

Answer 1

Put ln(x) = t, so that dx/x = dt. Then, we get

Integral t/(1 + t^2) dt = 1/2 ln(1 + t^2) + C, C a constant. So,

Integral ((ln x)/(x(1+ln^2 x))dx = (1/2) ln(1 + ln^2(x)) + C

Answer 2

call ln x = z so 1/x dx =dz and you get the
Int z/(1+z^2)dz = 1/2 ln(1+z^2) = 1/2[ln(1+(lnx)^2)]+C

Answer 3

Here is the math site:

http://mathworld.wolfram.com/

and here is his INTEGRATOR site:

http://integrals.wolfram.com/index.jsp