NDA2018MathematicsIndefinite IntegrationActual
What is dx 2^ x -1 equal to?
Options
- A(2^ x -1 )+ c
- B(1-2^ -x ) 2 +c
- C(2^ - x -1 ) 2 2 + c
- D(1+2^ - x ) 2 + c
Correct answer
B. (1-2^ -x ) 2 +c
Step-by-step solution
d x 2^x-1 = d x 1 2^ -x = 2^ -x 1-2^ -x d x Let 1-2^ - x = t 2^ - x 2= dt dx aligned & 2^ - x = 1 2 dt dx 2^ - x dx = dt 2 & 2^ - x 1-2^ - x dx = 1 2 dt t = 1 2 ( t )+ c & = 1 2 ( (1-2^ - x ) )+ c aligned