Looking for diffentiation and integration problems

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The discussion centers around finding challenging problems related to derivatives and antiderivatives, specifically mentioning the integral of sec(x)/(a-tan(x)). Participants suggest using resources like the CRC manual and Mathematica for solving tough integrals. Mathematica is identified as a commercial application for mathematical problem-solving, with a link provided for access. However, some participants emphasize that the focus should be on finding challenging problems rather than relying on software solutions. The conversation highlights the desire for difficult mathematical challenges rather than easy solutions.
jacy
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Hi,
I am looking for some tough problems on derivatives and anti derivates. Can someone suggest me a link, thanks.
 
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How about this:

\int\frac{sec(x)}{a-tan(x)} \ dx
 
hotvette said:
How about this:

\int\frac{sec(x)}{a-tan(x)} \ dx

thanks is there a link were i can find some more
 
The toughest integrals are no match for a handy CRC manual or mathematica!
 
Agnostic said:
The toughest integrals are no match for a handy CRC manual or mathematica!

what is mathematica is it a web site
 
You won't find this one in CRC. At least it isn't in mine. Mathematica, yes. Which is a commercial application for solving math problems.

http://www.wolfram.com/

But, Mathematica doesn't count in this case. I think the challenge is what is sought.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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