Integration... I need answers quick - XP Math - Forums

 XP Math - Forums Integration... I need answers quick

 09-04-2007 #1 alternet87 Guest   Posts: n/a Integration... I need answers quick Hi, I have a test tomorrow and I need to be able to Evaluate these integrals step by step. 1. $\int\frac{e^sqrt{x}}{sqrt{x}}dx$ 2. $\int_{e}^{e^2}x^3ln(x)dx$ 3. $\int\frac{x^2}{sqrt{16-x^2}}dx$ 4. $\int\frac{2}{x^2+1}dx$ 5. $\int\frac{x-2}{x^2-1}dx$ 6. $\int\frac{x^2-1}{x-2}dx$ 7. $\int tan^-^1(x)dx$ 8. $\int sec^2(\theta)tan^2(\theta) d(\theta)$ thanks a lot, if you want you can email me the work and answers to alternet87@hotmail.com Last edited by Sillysidley; 09-04-2007 at 04:06 PM..
 09-04-2007 #2 Temperal Guest   Posts: n/a First: Are you a robot? If not, I'll help you.
 09-05-2007 #3 alternet87 Guest   Posts: n/a no I am not a robot. thanks. I might just pay someone to do these because I need to have them done soon, and I have no idea how. if you can do it before I pay someone that would be AWESOME !!!!! thanks
 09-05-2007 #4 alternet87 Guest   Posts: n/a If someone finishes the first set of problems for me, here are just a couple more questions that aren't AS important, but would be nice too. 1.) Consider the function $F(x)=\int_1^{e^x} \frac{2ln(t)}{t}dt$ a.) Compute the derivative $\frac{dF(x)}{dx}$ using the Second Fundamental Theorem of Calculus. b.) Find F(0) and justify your answer showing work 2.) Suppose that $\int_1^x f(t) dt=x^2-2x+1$ Find F(x).
 09-05-2007 #5 Temperal Guest   Posts: n/a I'll try one of the easy ones for warmup; I'll do the rest, if I can, later. 8) This is quite easy. You just break it into sections, and use the product rule. $\int sec^2(\theta)tan^2(\theta) d(\theta)$ So, first work with $\int\sec^2{\theta}$ Is equal to $\int \ln{|sec{\theta}+\tan{\theta}|}^2 \text{ d}(\theta)$ as every good calc student knows. (Well, plus a constant, but we'll just stick that in at the end) now, $\int\tan^2{\theta}\text{ d}(\theta)$ is equal to $-\ln{|cos x|}^2$ Now apply the product rule $\int f(x)\cdot g(x)=(\int f(x))g(x)+f(x)(\int g(x))$ I'll leave you to solve. Last edited by Temperal; 09-05-2007 at 08:33 PM..
 09-05-2007 #6 alternet87 Guest   Posts: n/a i thought the product rule was only when finding the derivative, I need to find the anti-derivative. Maybe I am wrong but isn't $f'(x)$ the derivative of $f(x)$ The only thing I do know is that most of these problems can be solved by using Integration my substitution and Integration by Parts. I just don't know how to do it
 09-05-2007 #7 Temperal Guest   Posts: n/a The same rule applies to integration. And yeah, oops, I'll fix that.

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