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Question Number 67467 by ~ À ® @ 237 ~ last updated on 27/Aug/19

    Find    f(x)=∫_0 ^∞   (( tlnt)/((1+t^2 )^x )) dt

$$ \\ $$$$ \\ $$$${Find}\:\:\:\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\frac{\:{tlnt}}{\left(\mathrm{1}+{t}^{\mathrm{2}} \right)^{{x}} }\:{dt}\: \\ $$

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