# Homework Help: Integrate e^2x / SQRT (e^2x + 3)

1. May 20, 2010

### donleo

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

Integrate e^2x / SQRT [(e^2x) + 3)]

2. Relevant equations

3. The attempt at a solution

i know the solution, is: SQRT [(e^2x) + 3]

but i have no idea why. Please I need help

thank you

2. May 20, 2010

### eok20

Have you tried substitution?

3. May 20, 2010

### donleo

yes, t=e^2x + 3 but still nothing

4. May 20, 2010

### eok20

Ok, if t=e^2x + 3 then dt = 2e^2x, and what does the integral become in terms of t and dt?

5. May 20, 2010

### donleo

i have 1/2 (dt/ sqrt t)

so 1/2 t^(3/2) / (3/2)

then sqrt t / 3

then sqrt (e^2x+3)^3 / 3

its not the solution, it may be sqrt (e^2x+3)

6. May 20, 2010

### eok20

Close, you have 1/2(dt/sqrt(t)) = 1/2 t^(-1/2) dt. You integrated 1/2 t^(1/2) dt instead

7. May 20, 2010

### Gib Z

sqrt t is in the Denominator! So the power of t isnt 1/2, but actually... ?

8. May 20, 2010

### donleo

its true!!!!!! lol, it was my mistake, i forgot the change t^1/2 -> t^-1/2

thank you!!