Endpaper Integral Table form?

[hammy]

Hi guys, I'm trying to find an Endpaper Integral Table form that corresponds to the integral:

(4x)/((3x)-1)

I seriously cannot find anything. My book is telling me to use the sheet given to me, but I see nothing on here. I know I could probably just use long division and figure something out to integrate it that way, but it says to use the EIT.

 

[JeffM]

Hi guys, I'm trying to find an Endpaper Integral Table form that corresponds to the integral:

(4x)/((3x)-1)

I seriously cannot find anything. My book is telling me to use the sheet given to me, but I see nothing on here. I know I could probably just use long division and figure something out to integrate it that way, but it says to use the EIT.

I undoubtedly have a different book from yours (mine is dated March, 1961), but I have a standard form for the integral of x[sup:1yy0b0je]m[/sup:1yy0b0je](a + bx)[sup:1yy0b0je]n[/sup:1yy0b0je]. That seems to me to work for you, but obviously I studied integral calculus a LONG time ago.

 

[hammy]

Thanks for the help, sir.

Do you think I could use this formula from my book?

udu/(a + bu)

=

(1/(b^2)) (bu - a ln|a + bu|) + C

 

[Deleted member 4993]

Hi guys, I'm trying to find an Endpaper Integral Table form that corresponds to the integral:

(4x)/((3x)-1)

I seriously cannot find anything. My book is telling me to use the sheet given to me, but I see nothing on here. I know I could probably just use long division and figure something out to integrate it that way, but it says to use the EIT.

\(\displaystyle \int \frac{4x}{3x-1}dx \ = \ \frac{4}{3}\int \left [1 + \frac{1}{3x-1}\right]dx\)

Now continue...

 

[hammy]

I'll try to clarify my problem, I actually don't have any trouble finding the integral itself. I just need to table formula for it, because I guess the prof wants us to be able to find and use them efficiently.

 

[Deleted member 4993]

You could use the formula you stated before - keeping in mind that the given problem has a "constant" multiplier (4) on the numerator.

 

[hammy]

Could I just take out the 4 from the start?

 

[galactus]

I'll try to clarify my problem, I actually don't have any trouble finding the integral itself. I just need to table formula for it, because I guess the prof wants us to be able to find and use them efficiently.

My personal opinion, your professor needs to get with the times. With today's technology, integral tables are as obsolete as a slide rule.

If anything, he/she should be showing how to use the tech instead of antiquated tables.

 

[mmm4444bot]

Could I just take out the 4 from the start?

Yes. When integrating some "constant times a function", you may always pull-out the constant factor right away.

In other words, integral [constant * function] is the same as constant * integral[function].

This property of integration is elementary.

 

[JeffM]

I'll try to clarify my problem, I actually don't have any trouble finding the integral itself. I just need to table formula for it, because I guess the prof wants us to be able to find and use them efficiently.

My personal opinion, your professor needs to get with the times. With today's technology, integral tables are as obsolete as a slide rule.

If anything, he/she should be showing how to use the tech instead of antiquated tables.

I AM HURT. (By the way, I still HAVE a slide rule, which admittedly my son looks at as though it were a bullroarer or an atlatl.)

I scarcely remember ANY integral calculus, and I would be utterly lost without my integral tables. It's NOT nice to be mean to the elderly. My book has tables of Bessel Functions and Laplace Transforms and even Hyperbolic Bessel Functions. I do not know what any of them do, but it is nice to have them there in black and white in case I ever become enlightened.

 

[mmm4444bot]

I still HAVE a slide rule, which admittedly my son looks at as though it were a bullroarer

Is that because it's hanging from your belt by a string?

 

[JeffM]

Re:

I still HAVE a slide rule, which admittedly my son looks at as though it were a bullroarer

Is that because it's hanging from your belt by a string?

Not at all. Hanging from my belt is an elegant holster carrying my slide rule.