# Homework Help: Integration, help me please.

1. Aug 11, 2012

### XtremePhysX

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

Find:

2. Relevant equations

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

3. The attempt at a solution

I tried u=e^x

2. Aug 11, 2012

### micromass

And what did you get?? Please provide a complete attempt.

3. Aug 11, 2012

### XtremePhysX

I think I got it :)

$$\int \frac{dx}{\sqrt{e^{2x}-1}} \\ Let u^2 = e^{2x}-1  \\ \therefore 2u du=2e^{2x}dx \\ udu = e^{2x}dx \\ Now u^2+1=e^{2x}  from the substitution so\\ I=\int \frac{udu}{1+u^2} \cdot \frac{1}{u} \\ = \int \frac{du}{1+u^2} \\= \tan^{-1}(\sqrt{e^{2x}-1})+C$$

Micromass, can you give me some high school level or 1st year uni integrals to practice, I did all the ones in my exercise book, I need some challenging integrals, please :)

4. Aug 11, 2012

### micromass

Looks good!

Sure! I'll look for some challenging ones!
If you want to get a good response, you can always make a thread in https://www.physicsforums.com/forumdisplay.php?f=109 asking for some challenging integrals!

Let me look for some goodies.

5. Aug 11, 2012

### Dickfore

Try this one:
$$\int{\frac{dx}{\sqrt{1 + x^4}}}$$

6. Aug 11, 2012

### micromass

Here are some nice ones:

$$\int \sqrt{\tan(x)}dx$$

$$\int e^{\sin(x)}\frac{x\cos^3(x)-\sin(x)}{\cos^2(x)}dx$$

$$\int \frac{1}{1+\sin(x)}dx$$

$$\int \frac{5x^4+1}{(x^5+x^+1)^2}dx$$

7. Aug 11, 2012

### XtremePhysX

Thank you a lot, I will try my best, and then post my solutions here so you guys can check if they are right or wrong.

8. Aug 11, 2012

### XtremePhysX

(1)Answer for the first 1: $$\frac{log(sex(x)(sin(x)+cos(x))(\sqrt{2}\sqrt{tan(x)}+1)))}{2\sqrt{2}}+C$$ The working was very tedious, very hard integral.
(2) Hard :(
(3) Using a Weierstrass substitution, the answer is: $$-\frac{1}{t+1}+C$$
(4) Simple U-Substitution, let u=x^5+x^+1

I couldn't show full working because I'm very tired now :(

9. Aug 11, 2012

### XtremePhysX

Tried a lot with this one, but it is impossible !!!
Please show me a short simple way of doing it.

10. Aug 11, 2012

### micromass

I don't think that his integral even has an elementary solution... Maybe he made a typo??

$$\int \frac{1-4x^5}{(x^5-x+1)^2}dx$$

This has a very easy integral and it's obvious once you see it. But it's pretty hard to find.

11. Aug 13, 2012

### XtremePhysX

So how do you do this integral? It looks easy but substitutions aren't working :\$

12. Aug 13, 2012

### Bohrok

What substitutions did you try?

13. Aug 13, 2012