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MHT CET202121 Sep 2021Morning ShiftMathematicsIndefinite IntegrationActual

[1+2 x( x+ x)]^ 1 2 d x=

Options

  1. A[ x( x- x )]+ c
  2. B[ cosec x( x+ x)]+c
  3. C[ x( x+ x)]+c
  4. D[ x + x ]+ c

Correct answer

C. [ x( x+ x)]+c

Step-by-step solution

Let .I= [1+2 x( x+ x)]^ 1 / 2 d x= 1+2 ^2 x+2 x x )^ 1 / 2 d x [ (1+ ^2 x )+ ^2 x+2 x x ]^ 1 / 2 d x= ( ^2 x+ ^2 x+2 x x )^ 1 / 2 d x aligned & = [( x+ x)^2 ]^ 1 / 2 d x= ( x+ x) d x= x d x+ x d x & = | x+ x|- | x|+c = | x+ x| | x| +c & = [ x( x+ x)]+c aligned

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