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MHT CET20226 Aug 2022Morning ShiftMathematicsIndefinite IntegrationActual

The integral 3 x¹³+2 x¹¹ (2 x^4+3 x^2+1 )^4 d x is equal to (where C is a constant of integration.)

Options

  1. Ax¹² (2 x^4+3 x^2+1 )^3 +C
  2. Bx^4 (2 x^4+3 x^2+1 )^3 +C
  3. Cx^4 6 (2 x^4+3 x^2+1 )^3 +C
  4. Dx¹² 6 (2 x^4+3 x^2+1 )^3 +C

Correct answer

D. x¹² 6 (2 x^4+3 x^2+1 )^3 +C

Step-by-step solution

aligned & 3 x¹³+2 x¹¹ (2 x^4+3 x^2+1 )^4 d x= 3 x¹³+2 x¹¹ x¹⁶ (2+ 3 x^2 + 1 x^4 )^4 d x & =- 1 2 -6 x⁻³-4 x⁻⁵ (2+ 3 x^2 + 1 x^4 )^4 d x= -1 2 -1 3 (2+ 3 x^2 + 1 x^4 )⁻³+C & = 1 6 ( 2 x^4+3 x^2+1 x^4 )⁻³+C= x¹² 6 (2 x^4+3 x^2+1 )^3 +C aligned

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