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NDA2017MathematicsIndefinite IntegrationActual

What is dx x ( x ^7+1 ) equal to?

Options

  1. A1 2 | x ^7-1 x ^7+1 |+ c
  2. B1 7 | x ^7+1 x ^7 |+ c
  3. C| x ^7-1 7 x |+ c
  4. D1 7 | x ^7 x ^7+1 |+ c

Correct answer

D. 1 7 | x ^7 x ^7+1 |+ c

Step-by-step solution

dx x ( x ^7+1 ) = x ^6 x ^7 ( x ^7+1 ) dx Let x ^7= t 7 x^6 . d x= dt x^6 d x= d t 7 Then x^6 d x x^7 (x^7+1 ) = 1 7 d t t(t+1) aligned & = 1 7 [ 1 t dt - 1 t +1 dt ] & = 1 7 [ | t |- | t +1|]+ c & = 1 7 | t t +1 |+ c & = 1 7 | x ^7 x ^7+1 |+ c aligned

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