# Solving for indefinite integral

1. Mar 19, 2009

### 4littlepigs

1. The problem statement, all variables and given/known data

My daughter at college asked me to help her with these but it's been years since I've done them. I said I would try and then look over what she comes up with so any help would be great not so I can give her the answers but so I can tell her whether or not she on the right track and help her try to find it!

Problem 1
∫(t^3/2 + 2t^1/2 -4t^-1/2)dt=
∫t^3/2(dt) + 2∫t^1/2(dt) -4∫t^-1/2(dt)=
2/3t^5/2 +(2)(2)t^3/2 -(4)(2)t^1/2 +c=
2/3t^5/2+4t^3/2-8t^1/2+c

Am I anywhere near right with this one?

And the second one is:
∫sqrt(t)(t^2+t-1)dt
but I have no idea where to go with it...

Thanks to any and all that help and for any help you can give.

3. The attempt at a solution
What I have so far are above!

2. Mar 19, 2009

### Dick

The integral of t^n is t^(n+1)/(n+1). Apply that to t^(3/2) e.g. You get t^(5/2)/(5/2)=(2/5)*t^(5/2). Try and check your expression again. For the second one just multiply it out. E.g. sqrt(t)*t^2=t^(1/2)*t^(2)=t^(2+1/2)=t^(5/2). Now you've got the same kind of fractional powers as in the first part. You can also make your expression clearer with more parentheses. 2/3t^5/2 can be interpreted lots of different ways. Like ((2/(3t))^(5))/2.