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Question

Evaluate: 1(x1)(x2)dx

A
ln(|2x23x+2+2x3|)+c
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B
ln(|2x23x+2|)+c
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C
ln(|2x23x+22x+3|)+c
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D
ln(|x23x+2+2x3|)+c
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Solution

The correct option is A ln(|2x23x+2+2x3|)+c
1x1×x2dx
I=1x1×x2dx
=1x22xx+2dx
=1x23x+2dx
I=1(x3/2)2(5/2)2dx
as we know
dxx2a2=log|x+x2a2|+c
So, I=log(32+(x32)2(5/2)2)
=log(2x3+2x23x+2)+C1
I=log(2x23x+2+2x3)+C1
where C1=Clog2.

1165199_1060979_ans_6f0a113aca4d4df3b5dbdeabf419dd0a.jpg

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