Ex 7.7, 11 - Integrate root x2 - 8x + 7 dx - Class 12 - Integration by specific formulaes - Formula 7

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Ex7.7, 11 ∫1β–’γ€–βˆš(π‘₯2 βˆ’8π‘₯+7) " " γ€— 𝑑π‘₯ 1/2 (x - 4)√(π‘₯2 βˆ’8π‘₯+7) + 9 log |π‘₯βˆ’4+√(π‘₯2βˆ’8π‘₯+7)| + C 1/2 (x + 4)√(π‘₯2 βˆ’8π‘₯+7) + 9 log |π‘₯+4+√(π‘₯2βˆ’8π‘₯+7)| + C 1/2 (x - 4)√(π‘₯2 βˆ’8π‘₯+7) - 3√2 log |π‘₯βˆ’4+√(π‘₯2βˆ’8π‘₯+7)| + C 1/2 (x - 4)√(π‘₯2 βˆ’8π‘₯+7) + 9/2 log |π‘₯βˆ’4+√(π‘₯2βˆ’8π‘₯+7)| + C ∫1β–’γ€–βˆš(π‘₯^2βˆ’8π‘₯+7) 𝑑π‘₯γ€— =∫1β–’γ€–βˆš(π‘₯^2βˆ’2(4)(π‘₯)+7) 𝑑π‘₯γ€— =∫1β–’γ€–βˆš(π‘₯^2βˆ’2(4)(π‘₯) γ€–+(4)γ€—^2βˆ’(4)^2+7) 𝑑π‘₯γ€— =∫1β–’γ€–βˆš((π‘₯βˆ’4)^2βˆ’16+7) 𝑑π‘₯γ€— ∴ Option (D) is correct

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