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Statement 1: For $- 1 < a < 4$
$\int \frac{d x}{x^{2} + 2 (a - 1) x + a + 5} = λ \log | g (x) | + C,$ where $λ$ and $C$
are constants
Statement 2: For $- 1 < a < 4, f (x) = \frac{1}{x^{2} + 2 (a - 1) x + a + 5}$ is
a continuous function.

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STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

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detailed solution

Correct option is D

The discriminant of x2+2(a−1)x+a+5=0is 4(a−1)2−4(a+5)=4a2−3a−4<0 hence the integral ∫dxx2+2(a−1)x+a+5=λtan−1⁡g(x)+CSince the denominator is not zero for any value of x so f is acontinuous function.

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Statement 1: For −1<a<4∫dxx2+2(a−1)x+a+5=λlog⁡|g(x)|+C, where λ and Care constantsStatement 2: For −1<a<4,f(x)=1x2+2(a−1)x+a+5 is a continuous function.

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Statement 1: For $- 1 < a < 4$
$\int \frac{d x}{x^{2} + 2 (a - 1) x + a + 5} = λ \log | g (x) | + C,$ where $λ$ and $C$
are constants
Statement 2: For $- 1 < a < 4, f (x) = \frac{1}{x^{2} + 2 (a - 1) x + a + 5}$ is
a continuous function.