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Q.

If I1=∫1/etanxt1+t2 dt and I2=∫1/ecotxdtt1+t2 then the value of I1+I2 is

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a

1/2

b

1

c

e/2

d

(1/2) (e + 1/e)

answer is B.

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Detailed Solution

Putting t=1/u in I2 we haveI2=-∫etanxu du1+u2=-∫1/etanxu du1+u2+∫1/eeu du1+u2=-I1+12∫1/ee2u du1+u2so I1+I2=12logu2+11/ee=12log⁡e2+1−log⁡e2+1e2=12×2=1
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If I1=∫1/etanxt1+t2 dt and I2=∫1/ecotxdtt1+t2 then the value of I1+I2 is