how would i intergrate these.. how do i know when to use the chain rule when i m integrating these??
$\displaystyle \int xe^{-x^2}$
$\displaystyle \int e^{\frac{-y}{2}}$
$\displaystyle \int e^{2x}$
Chain rule for integration? Do you mean integration by parts?
u substitution will be sufficient for all of these.
$\displaystyle u = x^2$
$\displaystyle u=\frac{-y}{2}$
$\displaystyle u=2x$
Also, don't forget to put dx !
substitution, $\displaystyle u = x^2$
substitution, $\displaystyle u = - \frac y2$$\displaystyle \int e^{\frac{-y}{2}}~{\color{red}dy}$
or use the rule $\displaystyle \int e^{kx}~dx = \frac 1ke^{kx} + C$ for $\displaystyle k \ne 0$
see above$\displaystyle \int e^{2x}~{\color{red}dx}$
EDIT: Well, gee, thanks a lot Wingless!