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COMEDK2024MathematicsIndefinite Integration

9^x 1-81^x d x is equal to

Options

  1. A⁻¹ (9^x )+c
  2. B^9 ⁻¹ (9^x )+c
  3. C⁻¹ (81^x )+c
  4. D1 9 ⁻¹ (9^x )+c

Correct answer

D. 1 9 ⁻¹ (9^x )+c

Step-by-step solution

Let 9^x=t Differentiate both side w.r t. x aligned 9^x 9 d x & =d t 9^x d x & = d t 9 aligned aligned & Now, 9^x 1-9^ 2 x d x= 1 9 d t 1-t^2 & = 1 9 ⁻¹(t)+c [ 1 1-t^2 d t= ⁻¹ t ] & = 1 9 ⁻¹ (9^x )+c aligned

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