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AP EAMCET202022 Sep 2020Evening ShiftMathematicsIndefinite IntegrationActual

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

Options

  1. A|1+ ^2(x) |+c
  2. B- |1+ ^2(x) |+c
  3. C|1+ ^2(x) |+c
  4. D- |1+ ^2(x) |+c

Correct answer

D. - |1+ ^2(x) |+c

Step-by-step solution

aligned & 2 x ^2 x+2 ^2 x d x & = 2 x 1- ^2 x+2 ^2 x d x= 2 x 1+ ^2 x d x aligned Put, ^2 x=t aligned 2 x( & - x) d x=d t - & 2 x d x=d t & = -d t 1+t =- |1+t|+c [ t= ^2 x ] & =- |1+ ^2 x |+c aligned Hence, option (d) is correct.

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