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Question

If (x2+1)(x2+4)(x2+3)(x25)dx={1+f(x)(x2+3)(x25)}dx
x+Atan1(xA)+Blog(xlx+m)+K then which of the following is correct

A
A=143,B=2785,KR
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B
f(x)=7x2+19,A=3,KR
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C
l=m=5,L=1,KR
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D
All of these
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Solution

The correct option is D All of these
=1+7x2+19(x2+3)(x25)dx=(1+14(x2+3)+2741x25)dx
(x2+1)(x2+4)(x2+3)(x25)dx=x+143tan1(x3)+2785log(x5x+5)+K
(x2+1)(x2+4)(x2+3)(x25)dx=Lx+Atan1(xA)+Blog(xlx+m)+K
L=1,A=143,A=3,B=2785,KR
l=m=5;f(x)=7x2+19

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