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AP EAMCET201822 Apr 2018Morning ShiftMathematicsIndefinite IntegrationActual

( x-1 1+( x)^2 )^2 d x=

Options

  1. Ax 1+( x)^2 +c
  2. Bx x^2+1 +c
  3. Cx 1+( x)^2 +c
  4. D-x 1+( x)^2 +c

Correct answer

C. x 1+( x)^2 +c

Step-by-step solution

We have, aligned & I= x-1 1+( x)^2 ^2 d x &= e^t (t-1)^2 (t^2+1 )^2 d t, where t= x &= e^t t^2+1-2 t (t^2+1 )^2 d t &= e^t 1 t^2+1 + -2 t (t^2+1 )^2 d t &= e^t t^2+1 +C= x ( x)^2+1 +C . aligned

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