Integrate log(1+Xsquare)/(1+Xsquare) from zero to infinity

Hi

I will take question as

 ₀^infinity∫ log(1+x²)/(1+x²).dx

put x=tan@

=> dx = sec²@ d@

₀^pi/2∫ log (sec²@) d@

= -2 ₀^pi/2∫ log cos@ d@ = -2 (-pi/2 log2) = pi log2

because

₀^pi/2∫ log cosx dx = -pi/2 . log2

Solve it by properties of integral and check if you find problem then consult

Thanks

Anurag Kishore