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NDA2025MathematicsIndefinite IntegrationActual

What is dx 10^x + 10^ -x equal to?

Options

  1. A⁻¹(10^x) + c
  2. B( 10) ⁻¹(10^x) + c
  3. C1 10 ⁻¹(10^x) + c
  4. D(10^x + 10^ -x ) + c

Correct answer

C. 1 10 ⁻¹(10^x) + c

Step-by-step solution

Let I = dx 10^x + 10^ -x I = 10^x 10^ 2x + 1 dx Let 10^x = t 10^x 10 , dx = dt 10^x , dx = dt 10 I = 1 10 dt t^2 + 1 I = 1 10 ⁻¹(t) + c I = 1 10 ⁻¹(10^x) + c Answer: 1 10 ⁻¹(10^x) + c

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