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AP EAMCET202419 May 2024Evening ShiftMathematicsIndefinite IntegrationActual

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

Options

  1. A2 x+ (1+ x)+c
  2. Bx-2 (1+ x)+c
  3. C2 (1+ x)+ x+c
  4. D2 (1+ x)- x+c

Correct answer

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

Step-by-step solution

I= 2 2 x (1+ 2 x)(1+ 2 x) d x aligned & =2 1- ^2 x 1+ ^2 x (1+ 2 x 1+ ^2 x ) (1+ 1- ^2 x 1+ ^2 x ) d x & = (1- x) ^2 x (1+ x) d x Let x=t ^2 x d x=d t & = ( 1-t 1+t ) d t= (-1+ 2 1+t ) d t & =- x+2 (1+ x)+c . aligned

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