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Question

If (2x+3)dxx(x+1)(x+2)(x+3)+1=C1f(x), where f(x) is of the form of ax2+bx+c, then


(a+b+c) equals to .

A
5
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B
4
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C
3
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D
2
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Solution

The correct option is A 5
Let I=(2x+3)dxx(x+1)(x+2)(x+3)+1
=(2x+3)dx(x2+3x)(x2+3x+2)+1
Put x2+3x=t
(2x+3)dx=dt
I=dtt(t+2)+1
=dt(t+1)2=C1t+1=C1x2+3x+1
On comparing with C1ax2+bx+c, we get
a=1, b=3, c=1
a+b+c=5

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