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

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

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1 Answers

Anurag Kishore
37 Points
12 years ago

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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