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Question

(xln2+1)x(1+x2x)2 dx is equal to
(where C is a constant of integration)

A
ln(11+2x)+11+2x+C
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B
ln(x2x1+x2x)+11+x2x+C
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C
ln(x2x1+x2x)11+x2x+C
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D
ln(11+2x)+x2x1+x2x+C
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Solution

The correct option is B ln(x2x1+x2x)+11+x2x+C
Put x2x=t
dt=2x(1+xln2)dx
I=dtt(1+t)2=1+ttt(1+t)2 dt=(1t11+t1(1+t)2)dt
=ln|t|ln|1+t|+11+t+C
=ln(t1+t)+11+t+C=ln(x2x1+x2x)+11+x2x+C

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