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AP EAMCET20226 Jul 2022Evening ShiftMathematicsIndefinite IntegrationActual

1+2 x( x+ cosec x) d x=

Options

  1. A2 ( x 2 )+C
  2. B2 ( x)- ( cosec x+ x)+C
  3. C1 2 ( cosec x 2 + x 2 )+C
  4. D4 x 2 +C

Correct answer

A. 2 ( x 2 )+C

Step-by-step solution

aligned & Let I= 1+2 x( x+ cosec x d x . & = cosec ^2 x- ^2 x+2 ^2 x+2 x cosec x d x & = cosec ^2 x+ ^2 x+2 x cosec x d y & = ( cosec x+ x) d x & = | cosec x- x|+ | x|+C & = | 1- x x x |+C aligned aligned & = |2 ^2 x 2 |+ ^ C & = 2+ ^2 x 2 +C & =2 | x 2 |+C[ 2+C=C] aligned

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