derivable on 
with 
and 
be the origin, 
In space given the vessel formed by the revolution of the segment 
about 
-
When the vessel is filled with water, drain the water out such that the displacement per time is 
at the time of 
that is to say, if the total volume of the water drained out till the time 
is 
then 
holds. Find the time required for draining out water.
converge?
![$$\int_{-\sqrt[3]{2}}^{1}(x^3+x^6)(x^2+2x^5)dx$$](http://latex.artofproblemsolving.com/4/a/6/4a605ab36af1ef8fdb64fbbd5b4009f422112e9e.png)
![$$\int \frac{d}{dx}\left [ \frac{e^x}{\ln(x)} \right] \cdot \frac{\ln(x)}{e^x} dx$$](http://latex.artofproblemsolving.com/0/f/8/0f85946a83d7b8a210c470cf8876a2a701a0051d.png)
where 
and 
where 
.
satisfies 
and 
.![\[\lim_{n\to\infty} n \left( \;1 \; +\; \sum_{k=1}^n \frac{ (-1)^k}{k+1}
\sum_{1 \le j_1 \le j_2 \le \cdots \le j_k \le n}
a_{j_1} a_{j_2} \cdots a_{j_k} \right). \]](http://latex.artofproblemsolving.com/0/6/e/06e599d5270ba42a2a55cb995969be0dbf799392.png)
Y by audio-on, avyaank, PikaPika999, GodGodGodGodGoose
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