Solving Integral Problem with 2*e^sqrt(x)-2*e - Help Ylle

[Ylle]

I have this integral: (The first is the original, the one I need to solve)
http://www.absinthen.dk/math.jpg

Well, I have a program that can calculate it for me, but I need to do it in hand - but even though I keep trying, I just don't end up with the result my program says it is, which is:
2*e^sqrt(x)-2*e

I've been trying everything, but I going crazy very soon

I really hope you guys can give me a hint, of what may be wrong.


- Ylle

 

[Muzza]

I don't understand exactly what it is you've done to the integral, but...

$$\int e^{\sqrt{x}} x^{-1/2} dx = \int e^{\sqrt{x}} \cdot \frac{dx}{\sqrt{x}}$$

Let $$u = \sqrt{x}$$. Then $$\frac{du}{dx} = \frac{1}{2} \cdot \frac{1}{\sqrt{x}}$$, so 2du = 1/sqrt(x) dx. The integral turns in to:

$$\int e^{u} \cdot 2 du$$

After finding an antiderivative, putting in the limits should be easy... ;)

 

[Ylle]

hehe, and i don't understand what you are doing :D
I don't think they teach us to solve the integral the same way, as they do to you :(

But another example:
http://www.absinthen.dk/math2.jpg

This integral is solved correctly this time, and I've done the same thing as I would do in the one I gave you. But in the one I gave you, it just won't do as I want it to do

 

[HallsofIvy]

I really doubt that anyone "taught" you to replace "x" with "t" without saying what in the world the relationship between x and t is!

I also note that when you make the substitution, there is no "dt" in the integral. You are not being sufficiently careful- that may be where your problem is.

State clearly what substitution you are making and how you are replacing dx.