MATH 2411 #7: QUESTION 6

#7) 6a)

1. ANSWER: u = x ², du = 2x dx and v = ( 1 + 2x ² )
   SOLUTION: x ³ dx / ( 1 + 2x ² ) = ( x ²)( x dx / ( 1 + 2x ² ) ) = u dv. Therefore,u = x ², du = 2x dx and v = ( 1 + 2x ² )
   ( v was obtained using the substitution w = 1 + 2x ² . )
2. ANSWER: x ² ( 1 + 2x ² ) - 1/6 ( 1 + 2x ² ) ^3/2
   SOLUTION: .
   The last integral was evaluated using the substitution w = 1 + 2x ².
3. ANSWER: x ² ( 1 + 2x ² ) - 1/6 ( 1 + 2x ² ) ^3/2 +C