If ๐‘“โ€™(x) = ๐‘ฅ + 1/x , then ๐‘“(๐‘ฅ) is

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(a) x 2 + log |๐‘ฅ| + ๐ถย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย 

(b) x 2 /2+ log |๐‘ฅ| + ๐ถย ย ย ย ย ย 

(c) x/2 + log |๐‘ฅ| + ๐ถย  ย  ย  ย  ย  ย  ย  ย  ย  ย  ย  ย  ย  ย  ย 

(d) x/2 โˆ’ log |๐‘ฅ| + ๐ถ

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[MCQ Class 12] If ๐‘“'(๐‘ฅ) = ๐‘ฅ + 1/๐‘ฅ , then ๐‘“(๐‘ฅ) is  (a) x^2 + log - CBSE Class 12 Sample Paper for 2023 Boards

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Transcript

Question 5 If ๐‘“โ€™(๐‘ฅ) = ๐‘ฅ + 1/๐‘ฅ , then ๐‘“(๐‘ฅ) is (a) ๐‘ฅ^2 + log |๐‘ฅ| + ๐ถ (b) ๐‘ฅ^2/2+ log |๐‘ฅ| + ๐ถ (c) ๐‘ฅ/2 + log |๐‘ฅ| + ๐ถ (d) ๐‘ฅ/2 โˆ’ log |๐‘ฅ| + ๐ถNow, ๐‘“(๐‘ฅ) = โˆซ1โ–’ใ€–๐’‡^โ€ฒ (๐’™)๐’…๐’™ใ€— = โˆซ1โ–’(๐‘ฅ+1/๐‘ฅ)๐‘‘๐‘ฅ = โˆซ1โ–’ใ€–๐‘ฅ ๐‘‘๐‘ฅใ€—+โˆซ1โ–’ใ€–1/๐‘ฅ ๐‘‘๐‘ฅใ€— = ๐’™^๐Ÿ/๐Ÿ+๐’๐’๐’ˆโกใ€–|๐’™|ใ€—+๐‘ช So, the correct answer is (b)

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