COMEDK2023MathematicsIndefinite Integration
x d x 2(1+x)^ 3 / 2 is equal to
Options
- A2+x 1+x +C
- B2+x x 1+x +C
- Cx 1+x +C
- D- x 1+x +C
Correct answer
A. 2+x 1+x +C
Step-by-step solution
Let I= x d x 2(1+x)^ 3 / 2 On putting, 1+x=t , we get d x=d t aligned I & = (t-1) d t 2 t^ 3 / 2 = 1 2 [ t^ -1 / 2 d t- t^ -3 / 2 d t ] & = 1 2 [ t^ 1 / 2 1 / 2 - t^ -1 / 2 -1 / 2 ]+C & = 1 2 2 [ t + 1 t ]+C & = t+1 t +C= x+2 1+x +C aligned