1. ## integration problem

Question 1:

$\displaystyle \int {e^{-x}\ sinh(x)\ dx}$

Question 2:
$\displaystyle \int \frac {1}{\sqrt{1+x^2}}\ dx$

Assume:
$\displaystyle x = sinh (u)$
$\displaystyle dx = cosh(u) du$

Question 3:

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

Assume:
$\displaystyle x=tanh(u)$
$\displaystyle dx={sech^2} du$

2. Originally Posted by cron1003
Question 1:

$\displaystyle \int e^{-x} \sinh(x) dx$
change ... $\displaystyle \sinh(x) = \frac{e^x-e^{-x}}{2}$

3. Originally Posted by cron1003
This is the other question

Question 2:
$\displaystyle \int \frac {1}{\sqrt{1+x^2}}\ dx$

Assume:
$\displaystyle x = sinh (u)$
$\displaystyle dx = cosh(u) du$

Question 3:
$\displaystyle \int \frac{1}{1-x^2} dx$

Assume:
$\displaystyle x=tanh(u)$
$\displaystyle dx={sech^2} du$
Do what you are told to do (i.e. make the given substitutions) and then tell you stuck.

4. Question 3:

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

$\displaystyle \frac{1}{1-x^2}=\frac{1}{2}(\frac{1}{1-x}-\frac{1}{1+x})$
$\displaystyle \int \frac{1}{1-x^2} dx = \frac{1}{2}\int(\frac{1}{1-x}-\frac{1}{1+x})dx=\frac{1}{2}(ln|1-x|-ln|1+x|))=\frac{1}{2}ln|\frac{1-x}{1+x}|$

5. Originally Posted by cron1003

Question 1:

$\displaystyle \int {e^{-x}\ sinh(x)\ dx}$

Question 2:

$\displaystyle \int \frac {1}{\sqrt{1+x^2}}\ dx$

Assume:
$\displaystyle x = sinh (u)$
$\displaystyle dx = cosh(u) du$

Question 3:

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

Assume:
$\displaystyle x=tanh(u)$
$\displaystyle dx={sech^2} du$
duplicate post ...

http://www.mathhelpforum.com/math-he...n-problem.html

6. Originally Posted by cron1003
$\displaystyle \int e^{-x}\sinh x ~dx$
Use the fact $\displaystyle \sinh x = \frac{e^x-e^{-x}}{2}$