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But you need to EXPLAIN why it's a valid step. Without explanation many things could go down the drain... eg take a dodgy proof. The only way people could be convinced that your proof was right without you writing that bit down is by knowing that you NORMALLY would think of that step... which...

As long as the one you're taking out doesn't do dodgy stuff like go to 0 or infinity, I think you're fine. In this case, take out sec blah, which is a constant (ie 2)...

so why did you go? btw, there is a reason people go overseas..

you DON'T. remember, most random integrals you put down are very hard to do...

it gets hard. Although I'm old course..

hmm. real maths camps are better :-P

Hey! Basically you want to get rid of the top bit, since it's annoying. So letting u=e^(-x) du/dx=-e^(-x) So the integral becomes -Int(u/{1+(1/u)})du =-Int(u^2/(u+1))du =-Int(u-1+1/(u+1))du =-(u^2/2-u+ln(u+1)) =-(u^2/2)+u-ln(u+1) and sub u=e^(-x) back in. Shorter is what nike did...

indeed...

sigh.

Yeah... that's about right. only 1% of this post is relevant anyway, the other stuff only serves to confuse ppl...

for the last time.. this is not 4U. please please post it in the extracurricular board or the commerce board or the uni board but not here...

changed.

lol.. should. doesn't mean there's a nice way to do it

Moved...

basically, reducible means having factors. The factors in say Q have to have coefficients in Q etc... ditto R and C.

1A... that brings back sweet memories..

Talking about affinity's comment...

alternatively, just divide both sides by x^2 a la 4 Unit then use well known things like lim of sinx/x is 1, hence lim of sinx/x^2=0

Lol, that's all 3 of us..

so how exactly do you solve simultaneously? the point is, if you have a+b and ab, it's all well and fine, but the only way you get a, b is by solving the quadratic. You're confusing ability to solve n LINEAR simul eqn's in n variables with the ability to do it generally.... which doesn't exist...