MHT CET202611 April 2026Evening ShiftMathematicsIndefinite IntegrationActual
4^x(4^x + 4) , dx =
Options
- A1 2 [ 2^x 2 4^x + 4 + 2 |2^x + 4^x + 4 | ] + c
- B2^x 2 4^x + 4 + 2 |2^x + 4^x + 4 | + c
- C1 2 [ 2^x 2 4^x + 4 + |2^x + 4^x + 4 | ] + c
- D[ 2^x 4 4^x + 4 + |2^x + 4^x + 4 | ] + c
Correct answer
A. 1 2 [ 2^x 2 4^x + 4 + 2 |2^x + 4^x + 4 | ] + c
Step-by-step solution
I = 4^x(4^x + 4) , dx I = 2^x (2^x)^2 + 4 , dx Let 2^x = t , then 2^x 2 , dx = dt 2^x , dx = dt 2 I = 1 2 t^2 + 2^2 , dt Using the standard integral x^2 + a^2 , dx = x 2 x^2 + a^2 + a^2 2 |x + x^2 + a^2 | + c : I = 1 2 [ t 2 t^2 + 4 + 4 2 |t + t^2 + 4 | ] + c Substituting t = 2^x : I = 1 2 [ 2^x 2 4^x + 4 + 2 |2^x + 4^x + 4 | ] + c Answer: 1 2 [ 2^x 2 4^x + 4 + 2 |2^x + 4^x + 4 | ] + c