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Question

If we convert the denominator of the integral into a perfect square, 1x2 x + 1dx then the correct integral will be


A

1(x 1/2)2 + 1dx

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B

1(x 1/2)2 + 3/4dx

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C

1(x 1)2 + 1/2dx

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D

None of these

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Solution

The correct option is B

1(x 1/2)2 + 3/4dx


We know that ax2 + bx + c can also be written as a [(x + b/2a)2 + c/a b2/4a2] by completing squares, which we learnt in quadratic equations. We'll apply the same formula here. In the question given here, a = 1, b = -1, c = 1
So, x2 x + 1 = 1[(x 1/2)2 + 1 1/4]
or x2 x + 1 = [(x 1/2)2 + 3/4]
The given integral 1x2 x + 1dx can be written as 1(x 1/2)2 + 3/4dx


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