SOLUTION: Evaluate the following definite integral b ∫ x(x² + 3)² dx where a =1 and b = 6. a Round your answer to 1 decimal place.

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Question 1115246: Evaluate the following definite integral
b
∫ x(x² + 3)² dx where a =1 and b = 6.
a
Round your answer to 1 decimal place.
Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.
  6
  ∫ x(x² + 3)² dx  = 
  1

     6
= 1%2F2.∫ (x² + 3)^2*(dx²)  = 
     1

     6
= 1%2F2.∫ (x² + 3)²*d(x²+3)  =   // make substitution/replacement  x²+3 ---> t;  1 --->  1^2+3 = 4;  6 ---> 6^2+3 = 39.  You will get
     1

    39
= 1%2F2.∫ t^²*dt =   // it is just an elementary integral from the tables
     4

        |39
= 1%2F6.t%5E3 | = 1%2F6.%2839%5E3-4%5E3%29 = 9875.833.
        |4

Solved.