NDA2025MathematicsIndefinite IntegrationActual
What is dx 10^x + 10^ -x equal to?
Options
- A⁻¹(10^x) + c
- B( 10) ⁻¹(10^x) + c
- C1 10 ⁻¹(10^x) + c
- 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