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AP EAMCET202119 Aug 2021Morning ShiftMathematicsIndefinite IntegrationActual

∫ e x ( x + 3 ) ( x + 5 ) 3 d x =

Options

  1. Ae x ( x + 5 ) 2 + c
  2. Be x ( x + 5 ) 2 + c
  3. Ce x ( x + 3 ) 2 + c
  4. De x ( x + 3 ) 2 + c

Correct answer

A. e x ( x + 5 ) 2 + c

Step-by-step solution

Given that ∫ e x ( x + 3 ) ( x + 5 ) 3 d x = ∫ e x ( x + 5 - 2 ) ( x + 5 ) 3 d x = ∫ e x ( x + 5 ) - 2 ( x + 5 ) 3 d x = ∫ e x     1 x + 5 2   - 2 x + 5 3 d x We know that ∫ e x   f x   + f ' x   d x   =   e x f x   +   c Here f x   =   1 x + 5 2   &   f ' x   =   - 2 x + 5 3 = e x x + 5 2   +   c .

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