MHT CET202014 Oct 2020Morning ShiftMathematicsIndefinite IntegrationActual
x² (x+1)(x+2)² d x=
Options
- A|x+1|+ 4 x+2 +c
- B|x+1|- 4 x+2 + 3 (x+2)² +c
- C|x+1|+ 1 x+2 +c
- D|x+1|- 4 x+2 - 3 (x+2)² +c
Correct answer
A. |x+1|+ 4 x+2 +c
Step-by-step solution
I= x² (x+1)(x+2)² d x array l Let x ² ( x +1)( x +2)² = A x +1 + B x +2 + C ( x +2)² x ²= A ( x +2)²+ B ( x +1)( x +2)+ C ( x +1) When x =-2 , we get 4=- C C =-4 When x =-1 , we get 1= A A =1 array When x=0, A=1, C=-4 , we get 0=4+2 B-4 B=0 aligned I &= [ 1 x+1 - 4 (x+2)² ] d x &= d x x+1 -4 (x+2)⁻² d x &= |x+1|-4 (x+2)⁻¹ (-1) +c &= |x+1|+ 4 x+2 +c aligned