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Integrate log(1+Xsquare)/(1+Xsquare) from zero to infinity
Hi
I will take question as
0infinity∫ log(1+x2)/(1+x2).dx
put x=tan@
=> dx = sec2@ d@
0pi/2∫ log (sec2@) d@
= -2 0pi/2∫ log cos@ d@ = -2 (-pi/2 log2) = pi log2
because
0pi/2∫ log cosx dx = -pi/2 . log2
Solve it by properties of integral and check if you find problem then consult
Thanks
Anurag Kishore
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