imo class 12 indefinite integration

∫csc x dx is:

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∫csc x dx is:

  • A. ln|csc x − cot x| + C
  • B. ln|csc x + cot x| + C
  • C. −cot x + C
  • D. ln|tan(x/2)| + C

Answer: A) ln|csc x − cot x| + C

Explanation: Multiply numerator and denominator by (csc x − cot x). Substitute u = csc x − cot x. Result is ln|csc x − cot x| + C.

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