Class XII

∫ (logxⁿ/x)dx, n∈N, is equal to
  1. [{(log x)²}/2n]+C
  2. [{n(log x)²}/2]+C
  3. n(log x)²+C
  4. [(log x)/2n]+C
One value of∫f′(x) f x dx is
  1. f ‘ (x)
  2. f (x)
  3. {∫f(x)²}/2
  4. None of these
∫ √a2−x2 dx is equal to
  1. [(x/2) √a²−x²)]−[(a²/2) sin⁻¹(x/a)]+C
  2. [(x/2) √a²−x²)] + [(a²/2) sin⁻¹(x/a)]+C
  3. [(x/2) √a²−x²)] + [(a²/2) log x √a²−x² ]+ C
  4. [(a/2) √a²−x²)] + [(x²/2) log x √a²−x²] + C
Which of the following is different from ∫( 1/1+x²) dx ?
  1. (π/2)− cot⁻¹x+C
  2. − cot⁻¹x+C
  3. tan⁻¹x+C
  4. None of these
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