Class XII

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
∫ (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
If ∫f(x)dx=g(x)+C f x d x g x C then
  1. d/dx(g(x)+C)=f(x)
  2. g(x)= f (x)
  3. d/dx (f(x))=g(x)
  4. g(x) + f(x) = constant
∫(cos x/cos(x−a) dx is equal to
  1. sin a – sin a log | cos ( x – a) |
  2. sin a – sin a log | cos ( x – a) |
  3. x cos a+sin a log | cos (x–a) | + C
  4. x cos a – sin a log | cos ( x – a) |
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