NDA2021MathematicsIndefinite IntegrationActual
What is d x x (x^2+1 ) equal to?
Options
- A1 2 ( x^2 x^2+1 )+C
- B( x^2 x^2+1 )+C
- C3 2 ( x^2 x^2+1 )+C
- D1 2 ( x^2+1 x^2 )+C
Correct answer
A. 1 2 ( x^2 x^2+1 )+C
Step-by-step solution
aligned & I = d x x (x^2+1 ) & = d x x (x^2+1 ) & Let x^2+1=t x^2=t-1 & 2 x d s=d t & = 1 2 d t t(t-1) & = -1 2 [ 1 t - 1 (t-1) ] d t & = -1 2 [ 1 t d t- 1 (t-1) d t ] & = -1 2 [ (t)- (t-1)]+C & = 1 2 [ (t-1)- t]+C aligned aligned & = 1 2 ( t-1 t )+C & = 1 2 ( x^2 x^2+1 )+C aligned