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Question

The value of 2xx2+3x+2dx is
(where C is integration constant)

A
ln|x2|+2ln|x+1|+C
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B
2ln|x+2|+4ln|x+1|+C
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C
ln|x+2|+2ln|x1|+C
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D
4ln|x+2|2ln|x+1|+C
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Solution

The correct option is D 4ln|x+2|2ln|x+1|+C
2xx2+3x+2=2x(x+1)(x+2)2x(x+1)(x+2)=A(x+1)+B(x+2)2x=A(x+2)+B(x+1)(1)

Equating the coefficients of x and constant term, we obtain
A+B=22A+B=0
Solving these equations, we obtain
A=2, B=42x(x+1)(x+2)dx=[4(x+2)2(x+1)]dx=4ln|x+2|2ln|x+1|+C

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