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COMEDK2023MathematicsIndefinite Integration

4^x 1-16^x d x is equal to

Options

  1. A( 4) ⁻¹ 4^x+C
  2. B1 4 ⁻¹ (4^x )+C
  3. C1 4 ⁻¹ 4^x+C
  4. D4 4 ⁻¹ 4+C

Correct answer

C. 1 4 ⁻¹ 4^x+C

Step-by-step solution

aligned I & = 4^x 1-16^x d x & = 4^x 1- (4^x )^2 d x aligned On putting, 4^x=t , we get 4^x 4 d x=d t aligned 4^x d x & = d t 4 I & = 1 4 d t 1-t^2 & = 1 4 ⁻¹ t+C & = 1 4 ⁻¹ 4^x+C aligned

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