Recent content by dlthompson81

Homework Statement The sequence is 1 1 1 1 5 5 5 5 1 1 1 1 I need to find the formula for the sequence. Homework Equations The Attempt at a Solution I had a previous problem that was similar. It was a sequence of 1 5 1 5 1 5. I managed to get it with the formula of...

Homework Statement The problem is ∫e^x/(e^x)-1 to be evaluated from -1 to 1. Homework Equations The Attempt at a Solution I got the integral as ln|(e^x)-1| So, for the first part, evaluating from -1 to 0, with t being the limit at 0 I got this: ln|(e^t)-1| -...

Homework Statement Ok, this is a pretty simple integral, but I'm having trouble with the factoring. \int \frac{1}{x^{2}+2} According to the book, the answer is: \frac{1}{\sqrt{2}} tan^{-1}(\frac{x}{\sqrt{2})} Homework Equations The Attempt at a Solution So I need to get it in the form of...

Yes, I can integrate it from here, but since the problem is under the substitution review section in my book, I thought I would try to figure out how to do it with substitution. I usually write the dx whenever I work my problems out on my official paper, but I do avoid it on my scratch work...

Ok, I was wrong again. I thought I had it figured out. I have: \begin{equation}\int 1 + e^{-x}\end{equation} I set u = e^{-x} and du = -e^{-x} but then there is nothing for du to replace. I'm lost again.

Ok, after reviewing it some more I found my problem. The derivative of e^{-x} is actually -e^{-x}. I didn't realize I had to bring down the negative sign. And I did copy the answer wrong, it should be a -x exponent. My bad. Thanks for the help.

Homework Statement \begin{equation} \int \frac{e^{x}+1}{e^{x}}\end{equation} Homework Equations The Attempt at a Solution This problem comes out of the substitution section of my book, and the answer in the back of the book is x-e^{x}+C I started by changing the form to this...

Ok. I got it now. I wasn't thinking of e^{1} as a constant. Thanks for the help.

I don't understand how that rule applies exactly.

Homework Statement \begin{equation} \int_{-1}^{1} e^{u+1} \end{equation} Homework Equations The Attempt at a Solution I really seem to struggle with any problems with e in them. I think I may have missed some of the basic rules or something, but I can't seem to find what I missed...

After looking through the book, I found a table of integrals that has the inverse sin function. I don't seem to have the inverse ones in my notes. I don't know how I missed that. I got it figured out now. Thanks for the help.

Nope. We haven't had substitutions yet either. It looks like that is the next chapter we will cover if we stick to the order of the book.

I don't think we have covered anything on arcsin yet. I'm only in Calculus 2. If I should know that at this level, I guess one of my teachers let me down.

6(1-t^{2})^{-1/2} I tried to take the -1/2 exponent and add it to the 1-t^2 which gave me this: = 6(1^{1/2}-t^{3/2}) = 6^{1/2}-6t^{3/2} I figured I was doing it wrong, but my problem is that I'm not quite sure how to integrate 6(1-t^{2})^{-1/2} I'm not really sure how to change it...

Homework Statement [SIZE="5"]\int_{1/2}^{\sqrt{3}/2}\frac{6}{\sqrt{1-t^2}}dt Homework Equations The Attempt at a Solution Ok, this is an odd problem I'm working from the book. The book says the answer is \pi. First I tried getting rid of the fraction...