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MHT CET20228 Aug 2022Evening ShiftMathematicsIndefinite IntegrationActual

The integral ^2 x ^2 x d x ( ^5 x+ ^3 x ^2 x+ ^3 x ^2 x+ ^5 x )^2 is equal to (where C is a constant of integration).

Options

  1. A1 3 (1+ ^3 x ) +C
  2. B-1 3 (1+ ^3 x ) +C
  3. C-1 1+ ^3 x +C
  4. D1 1+ ^3 x +C

Correct answer

B. -1 3 (1+ ^3 x ) +C

Step-by-step solution

aligned & ^2 x ^2 x ~d x ( ^5 x+ ^3 x ^2 x+ ^3 x ^2 x+ ^5 x )^2 & ^2 x ^6 x ~d x ( ^5 x+ ^2 x+ ^3 x+1 )^2 [dividing N^r and D^r by ¹⁰ x ] & ^2 x ( ^2 x+1 )^2 ^2 x ~d x ( ^2 x+1 )^2 ( ^3 x+1 )^2 & ^2 x ^2 x ~d x ( ^3 x+1 )^2 & = -1 3 ( ^3 x+1 ) +c [ Let ^3 x+1=t ] aligned

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