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Question

Find the integral x+1x2+2x4dx

A
ln(x2+2x4)+C
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B
12ln(x2+2x)+C
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C
12ln(x2+2x4)+C
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D
12ln(x+1)+C
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Solution

The correct option is C 12ln(x2+2x4)+C
Given, f(x)=x+1x2+2x4
So, to integrate the given function we use substitution method.
Let t=x2+2x4 dtdx=2x+2=2(x+1)
Or, dt2=(x+1)dx
Thus, substituting this value in the given function we have,
x+1x2+2x4dx=12tdt=12lnt+C
12ln(x2+2x4)+C

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