## anonymous 5 years ago 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...?

1. anonymous

$\int\limits_{1}^{5}x(x^2+2)^5$

2. anonymous

I think that if you let u = (x^2 + 2) and du = 2x dx you can make the substitution as follows: $1/2 \int\limits_{1}^{5}u^{5} du$

3. anonymous

than to find the definte integral you just solve?

4. anonymous

oh ok. i understand now. that is the answer. thank you soo much! ^_^

5. 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.