# Some simple integral questions

1. May 10, 2009

### Emethyst

1. The problem statement, all variables and given/known data
Evaluate the following integrals: a) (2+x)/(2sqrtx) on the interval [4,9] b) (e^-x + 1)/e^-x on the interval [0,ln2] c) 1/(sqrtx - sqrt(x-1)) on the interval [1,5]

2. Relevant equations
N/A

3. The attempt at a solution
My teacher has said that these questions should be like other basic antiderivative questions, but they seem to be stumping me, probably because of the fractions involved. In short I have no idea where to start with these questions, even though (supposedly) the answers are not that hard to find. If anyone can get me started on the right path for these questions here it would be greatly appreciated, thanks in advance.

2. May 10, 2009

### Cyosis

For a) What is the derivative of $\sqrt{x}$. Do you see now what kind of substitution you can use?

b) Carry out the division. (a+b)c=a/c+b/c, it gives you a very simple integral.

c) Try multiplying by "1", with that I mean something of the form x/x, (x-1)/(x-1) etc. Do you see a good expression for "1"?

3. May 10, 2009

### Emethyst

Thanks for the help cyosis, I was able to get b) and c). I'm still confused on a), however. I know that the derivative is 1/2x^-1/2, but I don't know how to bring the (2+x) into the anitderivative though, unless you mean substitution using another variable.

4. May 10, 2009

### Cyosis

Make a substitution $u=\sqrt{x}$. You should recognize the derivative of this in the denominator of the integrand.