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Question

If1x2+x+1dx=asinh1(bx+c)+d, then descending order of a, b, c is

A
a, b, c
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B
b, c, a
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C
b, a, c
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D
c, a, b
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Solution

The correct option is C b, a, c
1x2+x+1dx=1x2+x+14+34dx
=1(x+12)2+(32)2
=log(x+12)+x2+x+1+c
=sinh1(2x+141)+c
=sinh1(23x+13)+c
Comparing with the given equation we get
a=1,b=23,c=13
Descending order of a,b,c is
b, a, c

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