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AP EAMCET202418 May 2024Morning ShiftMathematicsIndefinite IntegrationActual

cosec x 3 x+4 x d x=

Options

  1. A1 2 | x 3 x+4 x |+c
  2. B1 3 | x 3 x+4 x |+c
  3. C1 3 | 3 x+ x 3 x+4 x |+c
  4. D1 2 | x+4 x 3 x+4 x |+c

Correct answer

B. 1 3 | x 3 x+4 x |+c

Step-by-step solution

Let I = cosec x 3 x+4 x d x= cosec ^2 x 3 x+4 d x , Let 3 x+4=t aligned & -3 cosec ^2 x d x=d t & = -1 3 1 t d t=- 1 3 |t|+ C aligned = -1 3 |3 x+4|+C=- 1 3 | 3 x+4 x x |+ C = 1 3 | x 3 x+4 x |+C

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