NIMCET 2014 Question Paper with solutions

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Question : 20 of 120

Marks: +1, -0

The value of ∫

(x+1)/{x(xe^x+1)}

dx is equal to

log ${1+xe^x}/{xe^x}$ + C
log $[xe^x(1+xe^x)]$ + C
log $[1/{1+xe^x}]$ + C
log $[{xe^x}/{1+xe^x}]$ + C

Solution:

Let l = ∫

(x+1)/{x(xe^x+1)}

dx
Put

xxe^x

= t
⇒

(xe^x + e^x)

dx= dt
∴ l = ∫

{dt}/{t(t+1)}

=i

(1/t-1/{t+1})

dt
= log t - log (t + 1) + C
= log

t/{t+1}

= log

({xe^x}/{xe^x+1})

+ C

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