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Question

The value of the definite integral 11dx(1+ex)(1+x2) is


  1. π2

  2. π4

  3. π8

  4. 1


Solution

The correct option is B

π4


I=11dx(1+ex)(1+x2)   ....(i)

Put x=tdx=dt

I=11dt(1+et)(1+t2)

I=11(et)dt(1+et)(1+t2)

I=11(ex)dx(1+ex)(1+x2)  ...(ii)

Adding (i) and (ii)

2I=11dx1+x2=210dx1+x2

I=[tan1x]10=π4

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