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Question

For x>0, if f(x)=x1loget(1+t)dt then f(e)+f(1e) is equal to:

A
12
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B
1
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C
1
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D
0
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Solution

The correct option is A 12
f(e)+f(1e)=e1lnt1+tdt+1/e1lnt1+tdt=l1+l2
I2=1e1lnt1+tdt
Put t=1zdt=dzz2
I2=e1lnz1+1z×(dzz2)=e1lnzz(z+1)dz=e1lntt(t+1)dt

f(e)+f(1e)=e1lnt1+tdt+e1lntt(t+1)dt
=e1lnttdt
let lnt=u1tdt=du
=10u du=u2210=12

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