Recent content by bmanmcfly

Oops, forgot te minus here, not written down... Ok, thought I was doing that too simply. Thanks.

[SOLVED]Is this integral evaluation valid? Hi, so I started with \int \frac{\sin(x)\cos^2(x)}{5+\cos^2(x)}dxI made u=cos(x) dx=sin(x) leaving \int \frac{u^2}{5+u^2}dxAt this point I was thinking that it looked like an inverse tan, but I was lazy, so instead I tried...

[FONT=Times] Yes, that was what the equation simplified as... But you lost me a bit here... I get the putting this in terms of the limit, but how does $$I=4\lim_{t\to0}\left(\int_t^{\frac{\pi}{2}}\cos(x)+\cot(x)\,dx \right)$$ lead to $$I=4\lim_{t\to0}\left(1+\ln\left|\csc(t) \right|...

Now that I'm finally getting the hang of some of these integration techniques with complex functions, I've come across another hole. In my game here. That comes with the concept of resolving the definite integral of these complex functions. What happens is that they fluctuate and so can...

This example was too simple... The question would be appropriate as when, or what would you look for to substitute the ^ax or substituting the whole e^ax? Ok, I thought that would be a valid substitution, and much simpler than the alternative... Thanks, this was all helpful...

This was more general question... Like, for for example, you might see \int e^xdx Where you will substitute u=e^x anddu=e^xdx, where in another similar example you will substitute just the x portion. Another example that had me good was \int \frac{sin^2(x)dx}{1-\cos(x)}, where it turned out...

So, I'm gearing up for a final exam her, and while I handled learning the integration of trig,log and exponential functions... Nowthat I've got a good grasp of all these rules I'm getting lost in the sheer vastness of what I need to be aware of... For example, how do you, in general...

Now, the other part of the question; Is there any significant difference between \tan^{-1} , \cot, \and \arctan ??It seems that all mean the same thing? What's the reason to use one over the other? Cause to me it seems just preference.

Woops, I was thinking it would keep things more streamline... Not important. As for the integral, Thanks for the pointer, the limits would change to ln(e)- ln(1) or 1-0. let me know if I got you right... 3\int_{\ln(1)}^{\ln(e)}\frac{(\frac{1}{u}du)}{(1+u^2)} This gives...

[FONT=Times]I figured I would just add this new problem over here, rather than starting a new thread. Im looking to solve integration leading to arctan or arcsin results. \int_{1}^{e}\frac{3dx}{x(1+\ln(x)^2}) Looking at this, it feels like this has an arctan in the result, but I would have to...

That's actually a good technique I'll start doing that. Thanks again for the help, I thought I would find a similar simple example, but no luck. And the following questions carry on as a breeze... Which worries me, cause of its too easy I feel like in doing something wrong...

Ok, I think I get it... But is this a matter of simplification as it seems, or necessary?

Really?? So the \ln\left(e^x \right) was basically a trick to see how much you were paying attention... I'm curious, why is the int going from 0 to -2?

[FONT=Times]Hi again, so, I've been blasting away at the integration problems that I've been facing and just when I thought this term was going too easy, then I got to this one that kicked me in the left tooth. Problem: \int_{0}^{1}4\ln(e^x)e^{-2x^2}dx Attempted solution: Ok, first off we...

OOOOOHHHH! LMAO, another example of how dumb I am... I was trying to use the wrong axis for how I had things orientated, then I remembered if you make y1=y2 then you get the intersection, and everything else fell into place. So, the way that I would handle like my first post here, the...