KCET2025MathematicsIndefinite Integration
dx x ^2 ( x ^4+1 )^ 3 / 4 equals
Options
- A( x^4+1 x^4 )^ 1 4 +c
- B(x^4+1 )^ 1 4 +c
- C- ( x ^4+1 )^ 1 4 + c
- D- ( x^4+1 x^4 )^ 1 4 +c
Correct answer
D. - ( x^4+1 x^4 )^ 1 4 +c
Step-by-step solution
aligned & dx x ^2 ( x ^4+1 )^ 3 / 4 & = dx x ^5 (1+ 1 X ^4 )^ 3 / 4 1+ 1 x ^4 = T & -4 x ⁻⁵ dx = dt & =- 1 4 t ^ -3 / 4 dt =- 1 4 t ^ 1 / 4 1 4 + c =- (1+ 1 x ^4 )^ 1 / 4 aligned