anonymous
  • anonymous
if a u-substitute is used to evaluate elongated s with a high exponet of 5 and a low of 1 followed by x(x^2+2)^5dx, then the equivalent definte integral is...?
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
\[\int\limits_{1}^{5}x(x^2+2)^5\]
anonymous
  • anonymous
I think that if you let u = (x^2 + 2) and du = 2x dx you can make the substitution as follows: \[1/2 \int\limits_{1}^{5}u^{5} du\]
anonymous
  • anonymous
than to find the definte integral you just solve?

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anonymous
  • anonymous
oh ok. i understand now. that is the answer. thank you soo much! ^_^
anonymous
  • anonymous
Yeah! You take the antiderivative which, in this case, would be \[1/2\left[1/6u ^{6}\right]_1 ^5\] and then replace "u" with u=x^2 +2 and solve.

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