how would i intergrate these.. how do i know when to use the chain rule when i m integrating these??

$\displaystyle \int xe^{-x^2}$

$\displaystyle \int e^{\frac{-y}{2}}$

$\displaystyle \int e^{2x}$

2. Chain rule for integration? Do you mean integration by parts?

u substitution will be sufficient for all of these.

Originally Posted by Legendsn3verdie
$\displaystyle \int xe^{x^2}$
$\displaystyle u = x^2$
Originally Posted by Legendsn3verdie
$\displaystyle \int e^{\frac{-y}{2}}$
$\displaystyle u=\frac{-y}{2}$
Originally Posted by Legendsn3verdie
$\displaystyle \int e^{2x}$
$\displaystyle u=2x$

Also, don't forget to put dx !

3. Originally Posted by Legendsn3verdie
how would i intergrate these.. how do i know when to use the chain rule when i m integrating these??

$\displaystyle \int xe^{-x^2}~{\color{red}dx}$
substitution, $\displaystyle u = x^2$

$\displaystyle \int e^{\frac{-y}{2}}~{\color{red}dy}$
substitution, $\displaystyle u = - \frac y2$

or use the rule $\displaystyle \int e^{kx}~dx = \frac 1ke^{kx} + C$ for $\displaystyle k \ne 0$

$\displaystyle \int e^{2x}~{\color{red}dx}$
see above

EDIT: Well, gee, thanks a lot Wingless!