1. MIT integration bee questions

#1

[3x^3 -9]^(1/2)
______________
x

#2

[8x+6x^(5/2)]^(1/2)

I think we need to use substitution to solve these....anybody?

2. Originally Posted by mag6
#1

[3x^3 -9]^(1/2)
______________
x

#2

[8x+6x^(5/2)]^(1/2)

I think we need to use substitution to solve these....anybody?

The first one , substitute $x^3 = t$

The second one , first let $x = t^2$ then let $t^3 = u$ or you just let $x = u^{\frac{2}{3} }$

3. Originally Posted by simplependulum
The first one , substitute $x^3 = t$

The second one , first let $x = t^2$ then let $t^3 = u$ or you just let $x = u^{\frac{2}{3} }$
nope.....that's not working....none of them.

i tried taking u= x^3 - 3 in the first one but that's not working either.

4. For the first one, do $s=\sqrt{3x^3-9}$. For the second, $s=6x^{3/2}+8$.

For the first one, do $s=\sqrt{3x^3-9}$. For the second, $s=6x^{3/2}+8$.
how did you figure that out?!?! both of them are correct.....
how do you integrate them further?

6. Note that they're both essentially what simplependulum said, followed up by one more substitution.