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Ex 7.6, 24 - Integrate e^x sec x (1 + tan x) dx is (A) e^x cos x

Ex 7.6, 24 - Chapter 7 Class 12 Integrals - Part 2


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Ex 7.6, 24 ∫1▒𝑒^π‘₯ sec⁑π‘₯ (1+tan⁑π‘₯ )𝑑π‘₯ "ex" cos x + C (B) "ex" sec x + C (C) "ex" sin x + C (D) 𝑒π‘₯ tan x + C ∫1▒𝑒^π‘₯ sec⁑π‘₯ (1+tan⁑π‘₯ )𝑑π‘₯ = ∫1▒𝑒^π‘₯ (sec⁑π‘₯+sec⁑π‘₯ tan⁑π‘₯ )𝑑π‘₯ It is of the form ∫1▒〖𝑒^π‘₯ [𝑓(π‘₯)+𝑓^β€² (π‘₯)] γ€— 𝑑π‘₯=𝑒^π‘₯ 𝑓(π‘₯)+𝐢 Where 𝑓(π‘₯)=sec⁑π‘₯ 𝑓^β€² (π‘₯)=sec⁑π‘₯ tan⁑π‘₯ So, our equation becomes ∫1▒〖𝑒π‘₯ (sec⁑π‘₯+sec⁑π‘₯ tan⁑π‘₯ ) γ€— 𝑑π‘₯ = 𝑒^π‘₯ sec⁑π‘₯+𝐢 ∴ Option (B) is correct.

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