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MHT CET202124 Sep 2021Evening ShiftMathematicsIndefinite IntegrationActual

^3 x e^ ( x)^2 d x=

Options

  1. A^3 x 3 - ^5 x+c
  2. B^3 x 3 - ^5 x 5 +c
  3. C^3 x 3 + ^5 x 5 +c
  4. D^3 x+ ^5 x+c

Correct answer

B. ^3 x 3 - ^5 x 5 +c

Step-by-step solution

aligned & Let I= ^3 x e^ ( x)^2 d x & = ^3 x( x)^2 d x= ^2 x( x)^2 x d x & = ^3 x( x)^2 d x= ^2 x( x)^2 x d x aligned Put x=t x d x=d t I = ( t ^2- t ^4 ) dt = t ^3 3 - t ^5 5 + c = ^3 x 3 - ^5 x 5 + c

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