Consider $\int \frac{x^{3} + 3 x^{2} + 2 x + 1}{\sqrt{x^{2} + x + 1}} d x$ $= (a x^{2} + b x + c) \sqrt{x^{2} + x + 1} + λ \int \frac{d x}{\sqrt{x^{2} + x + 1}}$
Now, match the following lists and then choose the correct code :
Column – I Column – II
A) The value of ‘a’ (P) $- \frac{7}{24}$
B) The value of ‘b’ (Q) $\frac{1}{3}$
C) The value of ‘c’ (R) $\frac{1}{16}$
D) The value of $λ$ (S) $\frac{13}{12}$

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A – S; B – P; C – Q; D – R

A – Q; B – S; C – P ; D – R

A – Q; B – P; C – S ; D – R

A – S; B – Q; C – P; D – R

answer is C.

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Detailed Solution

Differentiate both sides with respect ‘x’ and compare the coefficients we get

$a = \frac{1}{3}, b = \frac{13}{12}, c = - \frac{7}{24} a n d λ = \frac{1}{16}$

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