The integral from [0,infinity) of lnx/(1+x^2)dx.

Question

Here's the question:

Find the value of the integral of lnx/(1+x^2)dx from 0 to infinity.
Follow the steps:
a). Make the substitution u = 1/x
b).Observe that the only number that satisfies the relation A = -A is zero.

If anyone can just show me how to find the integral of this equation I would be very greatful.  Thank you very much!

Answer 1

The definite integral cannot be found because the range 0 to infinity includes a value for which the integrand cannot be defined. In fact, ln(x/(1+x^2)) or ln(x)/(1+x^2) is minus infinity at x=0. The definite integral is equivalent to the area under the curve, and this cannot be determined where there is an asymptote. So the definite integral will be minus infinity, because the area lies below the axis.