- #1
XtremePhysX
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Homework Statement
Find:
Homework Equations
[tex]\int \frac{1}{\sqrt{e^{2x}-1}} dx[/tex]
The Attempt at a Solution
I tried u=e^x
XtremePhysX said:I tried u=e^x
XtremePhysX said:I think I got it :)
[tex]\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$\\ I=\int \frac{udu}{1+u^2} \cdot \frac{1}{u} \\ = \int \frac{du}{1+u^2} \\= \tan^{-1}(\sqrt{e^{2x}-1})+C[/tex]
Micromass, can you give me some high school level or 1 year uni integrals to practice, I did all the ones in my exercise book, I need some challenging integrals, please :)
micromass said:Here are some nice ones:
(1)[tex]\int \sqrt{\tan(x)}dx[/tex]
(2)[tex]\int e^{\sin(x)}\frac{x\cos^3(x)-\sin(x)}{\cos^2(x)}dx[/tex]
(3)[tex]\int \frac{1}{1+\sin(x)}dx[/tex]
(4)[tex]\int \frac{5x^4+1}{(x^5+x^+1)^2}dx[/tex]
Dickfore said:Try this one:
[tex]
\int{\frac{dx}{\sqrt{1 + x^4}}}
[/tex]
XtremePhysX said:Tried a lot with this one, but it is impossible !
Please show me a short simple way of doing it.
micromass said:I don't think that his integral even has an elementary solution... Maybe he made a typo??
What about this one:
[tex]\int \frac{1-4x^5}{(x^5-x+1)^2}dx[/tex]
This has a very easy integral and it's obvious once you see it. But it's pretty hard to find.
XtremePhysX said:So how do you do this integral? It looks easy but substitutions aren't working :$
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