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MHT CET202522 Apr 2025Evening ShiftMathematicsIndefinite IntegrationActual

^ 2 3 x cosec ^ 4 3 x ~d x=

Options

  1. A3 ^ -1 3 x+c , where c is the constant of integration
  2. B-3 ^ -1 3 x+c , where c is the constant of integration
  3. C-3 ^ -1 3 x+c , where c is the constant of integration
  4. D- 3 4 ^ -4 3 x+c , where c is the constant of integration

Correct answer

B. -3 ^ -1 3 x+c , where c is the constant of integration

Step-by-step solution

The integral I = ^ 2 3 x cosec ^ 4 3 x d x can be rewritten as I = ^2 x ^ 4 3 x d x by expressing x = 1 x and cosec x = 1 x , then multiplying numerator and denominator by ^2 x to simplify. Let u = x , so d u = ^2 x d x . Substituting yields I = u^ - 4 3 d u = -3 u^ - 1 3 + c . Reversing the substitution gives I = -3 ^ - 1 3 x + c . This matches option B. Final Answer: B

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