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∫1▒〖(𝑒^(3 log_𝑒⁡2𝑥 )+5𝑒^(2 log_𝑒⁡2𝑥 ))/(𝑒^(4 log_𝑒⁡𝑥 )+5𝑒^(3 log_𝑒⁡𝑥 )−7𝑒^(2 log_𝑒⁡𝑥 ) ) 𝑑𝑥〗,, is

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∫1▒〖(𝑒^(3 log_𝑒⁡2𝑥 )+5𝑒^(2 log_𝑒⁡2𝑥 ))/(𝑒^(4 log_𝑒⁡𝑥 )+5𝑒^(3 log_𝑒⁡𝑥 )−7𝑒^(2 log_𝑒⁡𝑥 ) ) 𝑑𝑥〗,, is