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Question

If x+12x1dx=f(x)2x1+C, where C is a constant of integration, then f(x) is equal to :

A
13(x+1)
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B
23(x+2)
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C
23(x4)
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D
13(x+4)
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Solution

The correct option is D 13(x+4)
I=x+12x1dx
Let 2x1=t2
dx=t dt
I=t2+12+1t t dt
=12(t2+3)dt

=12[t33+3t]+C

Put t=(2x1)1/2
I=12(2x1)1/2[2x13+3]+C
=12(2x1)1/2[2x+83]+C

Hence, f(x)=x+43

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