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If int((2x+3)dx)/(x(x+1)(x+2)(x+3)+1)=C-...

If `int((2x+3)dx)/(x(x+1)(x+2)(x+3)+1)=C-(1)/(f(x))` where f(x) is of the form of `ax^(2)+bx+c`, then the value of f(1) is

A

4

B

5

C

6

D

none

Text Solution

Verified by Experts

The correct Answer is:
B
`I=int(2x+3)/((x^(2)+3x)(x^(2)+3x+2)+1)dx`
Put `x^(2)+3x=t" "rArr(2x+3)dx=dt`
`rArr`
`I=int(dt)/(t(t+2)+1),int (dt)/((t+1)^(2))=C-(1)/(t+1)=C-(1)/(x^(2)+3x+1)`
`rArr" "f(1)=5`
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