MHT CET2008MathematicsIndefinite Integration
The value of x x ³ x d x is
Options
- A1 2 [ ² x- x ]+c
- B1 2 [x ² x- x ]+c
- C1 2 [x ² x+ x ]+c
- D1 2 [ ² x+ x ]+c
Correct answer
B. 1 2 [x ² x- x ]+c
Step-by-step solution
aligned x x ³ x d x &= x x 1 ³ x d x &= x x ² x d x Put x=t & ² x d x=d t and x &= ⁻¹ t aligned Then, it reduces to array l ⁻¹ t t d t= t² 2 ⁻¹ t- t² 2 (1+t² ) d t = x ² x 2 - 1 2 t+ 1 2 ⁻¹ t+c = x ( ² x-1 ) 2 - 1 2 x+ 1 2 x+c = 1 2 [x ² x- x ]+c array