Originally Posted by

**joseph_** I have to integrate

(t+1)(t^2+4)

from -3^1/2 to +3^1/2

I know the answer comes out to 10(3)^1/2, but I just can't get it. I tried re-writing it as the integral of t^3+t^2+4t+4 and that just made everything a mess. I also tried to do the integral of (t+1) time the integral of (t^2+4). However, I'm not sure if you can even do that. Can anyone help me with this problem?

Also, this one is giving me trouble (substitution). I'm not sure if I did it right..

Evaluate

10x^1/2

--------------dx

(1+x^3/2)^2

So I made

u=1+x^3/2

du=3/2x^1/2

So then I know that 20/3 will get me what I need.. so..

20/3 integral u^-2

20/3 u^-1/-1

Put it back in the original:

20/3 ((10x^1/2)(1+x^3/2)^-1 (*)

--------------------------

-1

Am I on the right track?