Manipal MET2014MathematicsIndefinite Integration
x^2-1 (x^4+3 x^2+1 ) ⁻¹ (x+ 1 x ) d x is equal to
Options
- A⁻¹ (x+ 1 x )+C
- B⁻¹ (x+ 1 x )+C
- C(x+ 1 x )+C
- D[ ⁻¹ (x+ 1 x ) ]+C
Correct answer
D. [ ⁻¹ (x+ 1 x ) ]+C
Step-by-step solution
Let, I= x^2-1 (x^4+3 x^2+1 ) ⁻¹ (x+ 1 x ) d x On dividing numerator and denominator by x^2 , we get I= 1- 1 x^2 (x^2+ 1 x^2 +3 ) ⁻¹ (x+ 1 x ) d x Put x+ 1 x =t aligned & (1- 1 x^2 ) d x & =d t and & aligned x^2+ 1 x^2 & =t^2-2 I & = d t (t^2-2+3 ) ⁻¹ t & = d t (1+t^2 ) ⁻¹ t & = ( ⁻¹ t )+C & = [ ⁻¹ (x+ 1 x ) ]+C aligned aligned