BITSAT2013MathematicsIndefinite IntegrationActual
( x ²-1 ) ( x ²+1 ) x ⁴+1 dx is equal to
Options
- A⁻¹ ( x²+1 2 x )+c
- B1 2 ⁻¹ ( x²+1 2 x )+c
- C1 2 ⁻¹ ( x²+1 2 )+c
- DNone of these
Correct answer
B. 1 2 ⁻¹ ( x²+1 2 x )+c
Step-by-step solution
I = x ² (1- 1 x ² ) dx x ² ( x + 1 x ) ( x ²+ 1 x ² )^ 1 / 2 Let x + 1 x = p (1- 1 x ² ) d x = dp I = dp p p ²-2 = 1 2 sec ⁻¹ p 2 = 1 2 ⁻¹ ( x ²+1 2 x )+ c