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Question

Evaluate 1(x1)(x2+1)dx

A
12log(x1)14log(x2+1)12tan1x+c
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B
12log(x1)+14log(x2+1)12tan1x+c
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C
12log(x1)12log(x2+1)12tan1x+c
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D
12log(x1)14log(x2+1)+tan1x+c
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Solution

The correct option is A 12log(x1)14log(x2+1)12tan1x+c
1(x1)(x2+1)dx=(1x2(x2+1)+12(x1))dx
=121xx2+1dx+121x1dx
=12(1x2+1xx2+1)dx+121x1dx
=12xx2+1dx121x2+1dx+121x1dx
=14log(x2+1)12tan1x+12log(x+1)
Hence, option 'A' is correct.

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