SOLUTION: Could someone please show me how to evaluate the following intergrals using the given substitutions? ((3x^2 + 6x)dx) / (x^3 + 3x^2 +11), substitution: x^3 + 3x^2 +11 Thanks,

Algebra ->  Expressions -> SOLUTION: Could someone please show me how to evaluate the following intergrals using the given substitutions? ((3x^2 + 6x)dx) / (x^3 + 3x^2 +11), substitution: x^3 + 3x^2 +11 Thanks,       Log On


   

Question 349447: Could someone please show me how to evaluate the following intergrals using the given substitutions?
((3x^2 + 6x)dx) / (x^3 + 3x^2 +11), substitution: x^3 + 3x^2 +11
Thanks,
-Nick.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let u=x%5E3%2B3x%5E2%2B11
du=%283x%5E2%2B6x%29dx
So then
+%28%283x%5E2+%2B+6x%29dx%29+%2F+%28x%5E3+%2B+3x%5E2+%2B11%29=du%2Fu
which can easily be integrated and then re-substituted.