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Question

Find the integral of dx(x+1)(x+2)

A
logx+2x+1+C
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B
log(x+1)+log(x+2)+C
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C
logx+1x+2+C
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D
logxx+2+C
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Solution

The correct option is C logx+1x+2+C
Let
1(x+1)(x+2)=Ax+1+Bx+2
1=A(x+2)+B(x+1)Ax+Bx+2A+B=1
Comparing the coefficient of x and constant on both sides,
A+B=0 and 2A+B=1
Solving the above two equations, we get
A=1 and B=1
dx(x+1)(x+2)=(1(x+1)1(x+2))dx
=log(x+1)log(x+2)+C=logx+1x+2+C

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