AP EAMCET201920 Apr 2019Morning ShiftMathematicsIndefinite IntegrationActual
( x^5 d x (x^2+x+1 ) (x^6+1 ) (x^4-x^3+x-1 ) = )
Options
- A( ₆ | x^6-1 x^6+1 |+c )
- B( 1 12 _e | x^6-1 x^6+1 |+c )
- C( 1 12 _e | x^4+1 x^4-1 |+c )
- D( _e | x^8+4 x^6-1 |+c )
Correct answer
B. ( 1 12 _e | x^6-1 x^6+1 |+c )
Step-by-step solution
Given integral ( aligned & x^5 d x (x^2+x+1 ) (x^6+1 ) (x^4-x^3+x-1 ) & (x^2+x+1 ) (x^4-x^3+x-1 )=(x-1) (x^3+1 ) & (x^2+x+1 ) & = (x^3-1 ) (x^3+1 )=x^6-1 & Given integral = x^5 d x (x^6+1 ) (x^6-1 ) & put x^6=t 6 x^5 d x=d t aligned ) then given integral ( aligned & = 1 6 d t (t+1)(t-1) = 1 12 _e | t-1 t+1 |+c & = 1 12 _e | x^6-1 x^6+1 |+c aligned ) Hence, option (2) is correct.