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MHT CET20227 Aug 2022Morning ShiftMathematicsIndefinite IntegrationActual

5 (x^6+1 ) x^2+1 ~d x= (Where C is a constant of integration.)

Options

  1. A5 (x^7+1 )+ (x^2+1 )+C
  2. Bx^5- 5 x^3 3 +5 x+C
  3. C5 x^7 7 +5 x+5 ⁻¹ x+C
  4. D5 ⁻¹ x+ (x^2+1 )+C

Correct answer

B. x^5- 5 x^3 3 +5 x+C

Step-by-step solution

aligned & 5 (x^6+1 ) x^2+1 ~d x= 5 (x^2+1 ) (x^4-x^2+1 ) x^2+1 ~d x & =5 (x^4-x^2+1 ) d x & =5 x^5 5 - x^3 3 +x +C & =x^5- 5 3 x^3+5 x+C aligned

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