Solve Integration Problems: Homework Help

[phantomprime]

Homework Statement

Homework Equations

n/a

The Attempt at a Solution

For the first one I tried to simplify it, though for some reason I don't think its the correct procedure.

 

[hotcommodity]

Can you show what you did for the first one? If people can see what you did, it'll be easier to help.

 

[phantomprime]

answer...attempted

1: I simplified the dominator to x(x^2 -1)then i said U was equal to that. Now i don't know if i am starting off right..my professor was talking about something on "Integral of rational functions by partial fractions" and he said solve by that using the different cases. I really don't know what he's talking about. I looked in the book and that doesn't help much. I see the cases and all..but nothing similar to these problems.I looked online too and that's no help

2)I said a^2=16 and a is 4
i simplified it using integral notation to 1/4tan^-1 (x/4) to = ln|x+sqrt(x^2 + 4^2)|

3&4)... I really don't know where to begin

5. I converted that to ln |x+ sqrt(x^2 -1)|..but somehow I know my attempts are wrong

 

[HallsofIvy]

1: I simplified the dominator to x(x^2 -1)then i said U was equal to that. Now i don't know if i am starting off right..my professor was talking about something on "Integral of rational functions by partial fractions" and he said solve by that using the different cases. I really don't know what he's talking about. I looked in the book and that doesn't help much. I see the cases and all..but nothing similar to these problems.I looked online too and that's no help

If your teacher suggested partial fractions and you don't know what he's talking about, you have a serious problem. "Partial fractions" is a standard way to deal with problems like this and apparently your teacher has already taught you that (or tried to). Completely factor the denominator [x(x-1)(x+1)] and write the fraction as a sum of fractions each having one factor as denominator. If you don't know how to do "partial fractions", look it up in your textbook.

2)I said a^2=16 and a is 4
i simplified it using integral notation to 1/4tan^-1 (x/4) to = ln|x+sqrt(x^2 + 4^2)|

3&4)... I really don't know where to begin

Once again, there is a standard method for dealing with integrals of products of trig functions. In particular, there is a simple method for products of sine and cosine where one of them is to an odd power. Look it up in your textbook.

5. I converted that to ln |x+ sqrt(x^2 -1)|..but somehow I know my attempts are wrong

HOW did you convert it to that? The calculus book I have beside me gives, in a table of integrals,
$$\int sin^{-1} u du= u sin^{-1} u+ \sqrt{1- u^2}+ C$$

 

[phantomprime]

If your teacher suggested partial fractions and you don't know what he's talking about, you have a serious problem. "Partial fractions" is a standard way to deal with problems like this and apparently your teacher has already taught you that (or tried to). Completely factor the denominator [x(x-1)(x+1)] and write the fraction as a sum of fractions each having one factor as denominator. If you don't know how to do "partial fractions", look it up in your textbook.

I know I have a serious problem in math, I don't need anyone to tell me that. Do you think I enjoy staying after class, asking people in class and even asking people online for help. I don't enjoy it, in fact I feel inferior becasue of it. I mean if one person can get it why can't I. I do it because it is required. So I can learn from it, I have done this with Physics as well and I mangaged to understand it. I have "Calculus of a Single variable" by james stuart. I look through it and yes it has partial fractions and all..but the thing is these problems are even numbered ones in the book. Even if I get an answer I don't know if its right or wrong. I wouldn't mind if there were odd so I can check them in the back.

 

[odie5533]

I know I have a serious problem in math, I don't need anyone to tell me that. Do you think I enjoy staying after class, asking people in class and even asking people online for help. I don't enjoy it, in fact I feel inferior becasue of it. I mean if one person can get it why can't I. I do it because it is required. So I can learn from it, I have done this with Physics as well and I mangaged to understand it. I have "Calculus of a Single variable" by james stuart. I look through it and yes it has partial fractions and all..but the thing is these problems are even numbered ones in the book. Even if I get an answer I don't know if its right or wrong. I wouldn't mind if there were odd so I can check them in the back.

If you are just looking to verify your answer, try http://integrals.wolfram.com/index.jsp. It won't help you solve the integrals though.

 

[hotcommodity]

I know I have a serious problem in math, I don't need anyone to tell me that. Do you think I enjoy staying after class, asking people in class and even asking people online for help. I don't enjoy it, in fact I feel inferior becasue of it. I mean if one person can get it why can't I. I do it because it is required. So I can learn from it, I have done this with Physics as well and I mangaged to understand it. I have "Calculus of a Single variable" by james stuart. I look through it and yes it has partial fractions and all..but the thing is these problems are even numbered ones in the book. Even if I get an answer I don't know if its right or wrong. I wouldn't mind if there were odd so I can check them in the back.

There's no reason to feel "inferior" just because you're having trouble on a calculus problem. Some of the best and brightest students come here to ask questions and refine their knowledge, and they do it because they care. You posted the question you did because you care about your work, and I find that to be very noble. If you're dissatisfied with an answer or explanation just keep asking until you find the answer you're looking for. No one here knows your name or where you go to school, so post as much as you'd like. If you still have questions just ask them :)