How do i integrate:
a) x^2*cos x
b) x^2*e^-x
If you could help me on either or both, would be great.
In both cases use integration by parts:
$\displaystyle \int u dv = uv - \int v du$
For example:
$\displaystyle \int x^2 cos(x) dx$
Let $\displaystyle u = x^2 \implies du = 2x dx$
Let $\displaystyle dv = cos(x) dx \implies v = sin(x)$
So
$\displaystyle \int x^2 cos(x) dx = x^2 sin(x) - \int 2x sin(x) dx$
The idea is to use the "u" to reduce the power of x in front of the other function.
Now use integration by parts on $\displaystyle \int x sin(x) dx$ using the same idea.
Problem b) is done the same way.
-Dan
$\displaystyle
\begin{aligned}
\int {x^2 e^{ - x} \,dx} &= \int {\left( {x^2 e^{ - x} + 2xe^{ - x} + 2e^{ - x} - 2xe^{ - x} - 2e^{ - x} } \right)\,dx}\\
&= \int {\left[ {e^{ - x} \left( {x^2 + 2x + 2} \right) - e^{ - x} \left( {2x + 2} \right)} \right]\,dx}\\
&= \int {\left[ { - e^{ - x} \left( {x^2 + 2x + 2} \right)} \right]^{\prime} \,dx} \hfill \\
&= - e^{ - x} \left( {x^2 + 2x + 2} \right) +k
\end{aligned}
$
Ahh ok, now I get it.
Hey Hacker, you'd really be a great value if you register there, 'cause you're a really good mathematician.
Actually you can use Google Language Tools to translate.
Anyway if you desire, I can help you with spanish so you can post there
P.S.: I'm not in the college yet, so I didn't select a math major