Calculus Integration help please -- involves sinh(x), e^x and roots

[Delta31415]

Homework Statement

[/B]
$$\int \left ( \frac{-1}{2*\sinh(x)*\sqrt{1-e^{2x}})} \right ) dx$$

or
http://www.HostMath.com/Show.aspx?Code=\int \left ( \frac{-1}{2*\sinh(x)*\sqrt{1-e^{2x}})} \right ) dx

Homework Equations

the sinh identity, which is (e^x-e^-x)/2

The Attempt at a Solution

Tried using the tables but am lost

btw how do I get latex to work?

 

[NFuller]

btw how do I get latex to work?

There's a button just below the reply box that says LaTex/BBcode Guides.

Tried using the tables but am lost

Here's a hint
$$\text{sinh}(x)=-\frac{1-e^{2x}}{2e^{x}}$$

 

[Delta31415]

There's a button just below the reply box that says LaTex/BBcode Guides.

Here's a hint
$$\text{sinh}(x)=-\frac{1-e^{2x}}{2e^{x}}$$

so it would similar to a rational function of sine that would have u = tan(x/2)
thanks

 

[andrewkirk]

To make latex work on this forum, enclose the code between $$ delimiters to display it on a line by itself, or between ## delimiters to include it within a line of ordinary text.

If you re-write $\sinh x$ as $-e^x(1-e^{2x})$ you should be able to change the integrand to an expression of the form $e^{-x}(1-e^{2x})^{k/2}$ for some integer $k$.

 

[Delta31415]

There's a button just below the reply box that says LaTex/BBcode Guides.

Here's a hint
$$\text{sinh}(x)=-\frac{1-e^{2x}}{2e^{x}}$$

btw how did you get to $$\text{sinh}(x)=-\frac{1-e^{2x}}{2e^{x}}$$ from $$\text{sinh}(x)=-\frac{e^{x}-e^{-x}}{2}$$

 

[NFuller]

btw how did you get to $$\text{sinh}(x)=-\frac{1-e^{2x}}{2e^{x}}$$ from $$\text{sinh}(x)=-\frac{e^{x}-e^{-x}}{2}$$

$$\text{sinh}(x)=\frac{e^{x}-e^{-x}}{2}=\frac{e^{x}}{e^{x}}\frac{e^{x}-e^{-x}}{2}=\frac{e^{2x}-1}{2e^{x}}=-\frac{1-e^{2x}}{2e^{x}}$$

 

[Delta31415]

$$\text{sinh}(x)=\frac{e^{x}-e^{-x}}{2}=\frac{e^{x}}{e^{x}}\frac{e^{x}-e^{-x}}{2}=\frac{e^{2x}-1}{2e^{x}}=-\frac{1-e^{2x}}{2e^{x}}$$

Thanks