1. integration problem

Question 1:

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

$

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

Assume:
$
x = sinh (u)
$

$
dx = cosh(u) du
$

Question 3:

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

Assume:
$
x=tanh(u)
$

$
dx={sech^2} du
$

2. Originally Posted by cron1003
Question 1:

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

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

3. Originally Posted by cron1003
This is the other question

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

Assume:
$
x = sinh (u)
$

$
dx = cosh(u) du
$

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

Assume:
$
x=tanh(u)
$

$
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:

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

$\frac{1}{1-x^2}=\frac{1}{2}(\frac{1}{1-x}-\frac{1}{1+x})$
$
\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:

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

Question 2:

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

Assume:
$
x = sinh (u)
$

$
dx = cosh(u) du
$

Question 3:

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

Assume:
$
x=tanh(u)
$

$
dx={sech^2} du
$
duplicate post ...

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

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