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Question

Solve :

(lnx1(lnx)2+1)2dx

A
xx2+1+c
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B
lnx(lnx)2+1+c
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C
x(lnx)2+1+c
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D
ex(xx2+1)+c
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Solution

The correct option is C x(lnx)2+1+c
Let I=(lnx1(lnx)2+1)2dx

Put lnx=tx=etdx=etdt

I=et(t1t2+1)2dt=et1t2+12t(t2+1)2dt

we know that ex(f(x)+f(x))dx=exf(x)+c where f(x)=1t2+1,f(x)=2t(t2+1)2

I=ett2+1+c=x(lnx)2+1+c

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