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Question 46
If
$$\alpha = \int_{0}^{1} \left(e^{9x + 3 \tan^{-1}x}\right)\left(\frac{12 + 9x^2}{1 + x^2}\right) dx$$
where $$\tan^{-1}x$$ takes only principal values, then the value of $$\left(\log_e |1 + \alpha| - \frac{3\pi}{4}\right)$$ is
Correct Answer: 9
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