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Question

lf dxxx3= Alog |x21x2|+c then A=

A
2
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B
12
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C
23
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D
13
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Solution

The correct option is A 12
dxxx3=dxx(1x2)=dxx(1x)(1+x)
1x(1x)(1+x)=Ax+B1x+C1+x;A=1;B=12;C=12
=1x+=(1/2)1x+(1/2)1+x
[1x+1/21x+1/21+x]dx=log x12 log(1x) 12 log(1+x)+c
log x[log(1x 2)1/2]+c
=log∣ ∣x(1x2)1/2∣ ∣+c
=12 logx21x2+c
A=12

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