Which substitution can I use to help me prove that the integral of ln (x) / (1 + x^2) between 0 and 1 is identical to -1 * the same integral between 1 and infinity?
Which substitution can I use to help me prove that the integral of ln (x) / (1 + x^2) between 0 and 1 is identical to -1 * the same integral between 1 and infinity?
The first thing I notice is that the substitution u= 1/x changes x= 0 to 1 into u= infinity to 1. du= so . The only "tricky" part is recognizing the and that is not all that "tricky"!
The first thing I notice is that the substitution u= 1/x changes x= 0 to 1 into u= infinity to 1. du= so . The only "tricky" part is recognizing the and that is not all that "tricky"!
Great thanks, you're right it does seem a lot less tricky now I can see it working