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