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If f (x) = $\int_{0}^{x}e^{t x-t^{2}} dt$ prove that

f(x) = $\int_{0}^{x}e^{\frac{x^{2}-t^{2}}{4}} dt$

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$\log_{2}\left(\cos^{2}\left(x\right)+\sin\left(x\right)\right)$

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Mathematical Expressions

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1. Cyclohexanol on oxidation gives (A). (A) on reaction with (CH₃)₂NH and subsequent hydrogenation with H₂Ni followed by heating gives (B) .(B) is first treated with CH₃I and then with AgOH which gives (C). (C) on heating upto 150 °C gives (D) . Identify (A) ,(B) ,(C) & (D) .

2. Ph-COOCH₃ + CH₃CH₂COOCH₃is first treated with C₂H₅ONa and with H⁺ which gives (A).

(A) on addtion of H₃O⁺gives (B) +(C ) .Mixture on heting gives (D) & CO₂

identify all compounds

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