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Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Q)

$\int \large\frac{2x^2+3}{(x^2-1)(x^2+4)}$$dx=a \log \bigg(\large\frac {x+1}{x-1} \bigg)+6 \tan ^{-1} \bigg( \large\frac{x}{2}\bigg)+c$ find the value of a and b?

$(a)\;(\frac{-1}{2},\frac{1}{2}) \\(b)\;(\frac{1}{2},\frac{-1}{2}) \\(c)\;(-1,1) \\ (d)\;None$

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A)
$\int \large\frac{dx}{x^2-1} +\int \large\frac{dx}{x^2 +4}$
=> $\large\frac{1}{2}$$ \log \bigg( \large\frac{x+1}{x-1}\bigg) +\frac{1}{2} $$\tan ^{-1} \large\frac{x}{2} +c$
$(\large\frac{-1}{2},\frac{1}{2})$
Hence a is the correct answer.
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