Question 5 If ๐โ(๐ฅ) = ๐ฅ + 1/๐ฅ , then ๐(๐ฅ) is (a) ๐ฅ^2 + log |๐ฅ| + ๐ถ (b) ๐ฅ^2/2+ log |๐ฅ| + ๐ถ (c) ๐ฅ/2 + log |๐ฅ| + ๐ถ (d) ๐ฅ/2 โ log |๐ฅ| + ๐ถNow,
๐(๐ฅ) = โซ1โใ๐^โฒ (๐)๐ ๐ใ
= โซ1โ(๐ฅ+1/๐ฅ)๐๐ฅ
= โซ1โใ๐ฅ ๐๐ฅใ+โซ1โใ1/๐ฅ ๐๐ฅใ
= ๐^๐/๐+๐๐๐โกใ|๐|ใ+๐ช
So, the correct answer is (b)
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