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COMEDK2016MathematicsIndefinite Integration

cosec x ² (1+ x 2 ) d x=

Options

  1. A- [1+ x / 2]+c
  2. B²[1+ x / 2]+c
  3. C[1+ x / 2]+c
  4. D²[1+ x / 2]+c

Correct answer

C. [1+ x / 2]+c

Step-by-step solution

Let I= cosec x ² (1+ array l x 2 array ) d x Put 1+ x 2 =t - 1 x 2 ² x 2 d x 2 =d t d x 2 x 2 x 2 =d t d x x =d t aligned & cosec x d x=d t So, I &= d i ² t = ² t d t= t+c &= (1+ x 2 )+i aligned

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