Recent content by James2

I have an equation, (5n + 2) = 2[(5/2)n + 1] I know this is true from the basis step. Then I asume n = k now I must prove n = k + 1. So, (5k + 2) = 2[(5/2)k + 1] Alright then, I try to substitute k + 1 in and add it or something so I get... 2[(5/2)k + 1] + [5(k + 1) + 2] = 2 [(5/2)(k + 1) + 1]...

Everything I read confuses me, it tells me to do something different everytime...

How do I prove a formula/rule or something by mathematical induction? Please give me a few examples or resources and explain it as best you can because I think I'm messing up some how.

Hello, I know all my algebra, trig, and I'm still fine tuning calculus and I've solved ODEs using the Laplace transform. Now, my question is... what else must I know to study Tensor calculus/Tensor Analysis? I really want to know so that I have a true understanding of relativity(the famous...

Whoa, this here is kicking me hard! Okay, so I've got everything pretty well down until... stuff like... \int \frac{3x + 32}{x^{2}-16x + 64}dx So, I get how to factor the denominator, but then what? The above won't factor... Also, I read that if the degree of the numerator is higher than the...

Guys I'm actually stuck on an integration problem involving the "u du rule" thing. It's just a little confusing; just one question, if I take du do I add it to the other part of du or do I replace the other stuff that isn't in u?

Okay I figured it out and worked a practice problem, the answers are at the back of the book but... I got: -\frac{(cos2x + 1)^{3/2}}{3/2} + C However, the answer to the practices in the back of the book says it is over 3 not 3/2? What happened here, I'm sure it's algebraic but still...

Oh wait I don't add it... I replace it? OR DO I ADD IT? Lol I'm confusing myself now.

Well in regards to one of the posts I saw earlier, I don't think I actually learned an entire semester, but it sure felt like it by the sheer amount of problems! Anyway, no, I am definitely not neglecting Algebra study at all. I do my homework the instant it is assigned and pay attention in...

Well actually one last thing, what happens to stuff that isn't a part of u? Like the x^2 outside of sqrt(u)?

Yes, I know 1/12(12)=1 and sure, sqrt(u). Oh wait... du means... derivative of u... okay but what happens to the things that aren't part of u?

Um I think this is the derivative.. \frac{du}{dx} = 12x^{2}e^{4x^{3}} OH OH OH! I'M SUPPOSED TO TAKE THE DERIVATIVE OF U THEN ADD IT TO THE OTHER PART? Right? And when do I have to move a constant factor outside the integral?

Seriously, somebody, I feel dumb because I am not getting this like am I supposed to find the derivative of u then add/multiply by the other thing?? UHHHHH...

So wait, I have to find the derivative of the exponent then add it to the terms in du? Like, there was an x^2 so I add 12x^2 to that and then take the reciprocal of 12 and move it outside the integral?

So, um, I am getting confused on integration problems where you have to do something with "a constant factor of n". Like, this example... \int\sqrt{1 + e^{4x^{3}}}e^{4x^{3}}x^{2}dx Then the example says to match it to the formula \int u^{n}du Okay... so it does that, but then...