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AP EAMCET202123 Aug 2021Morning ShiftMathematicsIndefinite IntegrationActual

(x+1)(x+2)^4(x+3) d x is equal to

Options

  1. A(x+1)^2 2 + (x+2)^2 5 + (x+3)^2 2 +C
  2. B(x+2)^7 7 - (x+2)^5 5 +C
  3. C(x+2)^7 7 + (x+2)^5 5 +C
  4. D(x+3)^7 7 - (x+3)^5 5 +C

Correct answer

B. (x+2)^7 7 - (x+2)^5 5 +C

Step-by-step solution

Let x+2=t , then d x=d t aligned I & = (t-1)(t)^4(t+1) d t= (t^2-1 ) t^4 d t & = (t^6-t^4 ) d t & = t^7 7 - t^5 5 +C & = (x+2)^7 7 - (x+2)^5 5 +C aligned

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