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COMEDK2013MathematicsIndefinite Integration

d x x (x⁷+1 ) is equal to

Options

  1. A( x⁷ x⁷+1 )+c
  2. B1 7 ( x⁷ x⁷+1 )+c
  3. C( x⁷+1 x⁷ )+c
  4. D1 7 ( x⁷+1 x⁷ )+c

Correct answer

B. 1 7 ( x⁷ x⁷+1 )+c

Step-by-step solution

Let aligned I &= 1 x (x⁷+1 ) d x &= x⁶ x⁷ (x⁷+1 ) d x aligned Put x⁷=t 7 x⁶ d x=d t aligned I &= 1 7 d t(t+1) = 1 7 ( 1 t - 1 t+1 ) d t &= 1 7 [ t- (t+1)]+c &= 1 7 ( t t+1 )+c= 1 7 ( x⁷ x⁷+1 )+c aligned

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