Manipal MET2015MathematicsIndefinite Integration
1-x^2 (1+x^2 ) 1+x^4 d x is equal to
Options
- A2 ⁻¹ 2 x x^2+1 +C
- B1 2 ⁻¹ 2 x x^2+1 +C
- C1 2 ⁻¹ 2 x x^2+1 +C
- DNone of these
Correct answer
B. 1 2 ⁻¹ 2 x x^2+1 +C
Step-by-step solution
Let aligned I & = 1-x^2 (1+x^2 ) 1+x^4 d x & = 1 x^2 -1 (x+ 1 x ) x^2+ 1 x^2 d x aligned aligned & =- 1 (x+ 1 x ) (x+ 1 x )^2-( 2 )^2 d (x+ 1 x ) & = 1 2 cosec ⁻¹ ( x+ 1 x 2 )+C & = 1 2 ⁻¹ ( 2 x x^2+1 )+C aligned