integral problem, please respond soon: int 4 dx / x ln(5x)

[jamiecooks1232]

hello! I have a question regarding a problem for my calculus 141 class which is due tomorrow (dont worry, were allowed outside help so this isnt cheating). the problem is evaluate the indefinite integral:
[FONT=MathJax_Main]\L[/FONT][FONT=MathJax_Size1]∫[/FONT][FONT=MathJax_Main]4[/FONT][FONT=MathJax_Math-italic]d[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Math-italic]l[/FONT][FONT=MathJax_Math-italic]n[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]5[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main])[/FONT]\L∫4dxxln(5x)
or with S representing the symbol for integral
S 4 dx / x ln(5x)
What I did which I think should be right but according to the math page isnt is move 4 to the front, set u=ln (5x) so du=5/5x dx which becomes du=1/x dx. so the 1/x in the problem is taken care of and the integral becomes 4x S 1/u du which becomes 4X ln(u) du or 4 ln(ln(5x)). is there another way to do this? or what am i doing wrong as web ct doesnt accept this answer. id really appreciate any help, preferably tonight as its due tomorrow though i know this is asking for a lot. [/code]

 

[Deleted member 4993]

hello! I have a question regarding a problem for my calculus 141 class which is due tomorrow (dont worry, were allowed outside help so this isnt cheating). the problem is evaluate the indefinite integral:
[FONT=MathJax_Main]\L[/FONT][FONT=MathJax_Size1]∫[/FONT][FONT=MathJax_Main]4[/FONT][FONT=MathJax_Math-italic]d[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Math-italic]l[/FONT][FONT=MathJax_Math-italic]n[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]5[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main])[/FONT]\L∫4dxxln(5x)
or with S representing the symbol for integral
S 4 dx / x ln(5x)
What I did which I think should be right but according to the math page isnt is move 4 to the front, set u=ln (5x) so du=5/5x dx which becomes du=1/x dx. so the 1/x in the problem is taken care of and the integral becomes 4x S 1/u du which becomes 4X ln(u) du or 4 ln(ln(5x)). is there another way to do this? or what am i doing wrong as web ct doesnt accept this answer. id really appreciate any help, preferably tonight as its due tomorrow though i know this is asking for a lot. [/code]

Does your problem look like this:

\(\displaystyle \displaystyle{\int {\dfrac{4 \ dx}{x\ ln(5x)}}\ }\)

or Does your problem look like this:

or \(\displaystyle \displaystyle{\int {\dfrac{4 \ dx}{x}\ ln(5x)}\ }\)

something else!!

 

[Dr.Peterson]

hello! I have a question regarding a problem for my calculus 141 class which is due tomorrow (dont worry, were allowed outside help so this isnt cheating). the problem is evaluate the indefinite integral:
[FONT=MathJax_Main]\L[/FONT][FONT=MathJax_Size1]∫[/FONT][FONT=MathJax_Main]4[/FONT][FONT=MathJax_Math-italic]d[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Math-italic]l[/FONT][FONT=MathJax_Math-italic]n[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]5[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main])[/FONT]\L∫4dxxln(5x)
or with S representing the symbol for integral
S 4 dx / x ln(5x)
What I did which I think should be right but according to the math page isnt is move 4 to the front, set u=ln (5x) so du=5/5x dx which becomes du=1/x dx. so the 1/x in the problem is taken care of and the integral becomes 4x S 1/u du which becomes 4X ln(u) du or 4 ln(ln(5x)). is there another way to do this? or what am i doing wrong as web ct doesnt accept this answer. id really appreciate any help, preferably tonight as its due tomorrow though i know this is asking for a lot. [/code]

I think your work is this:

\(\displaystyle \displaystyle \int \frac{4 \ dx}{x\ ln(5x)} = 4 \int \frac{du}{u} = 4 ln(u) = 4 ln(ln(5x))\)

That's just what I'd do (except that, of course, I'd add "+ C" at the end).

You can check by differentiating your answer.

I'm wondering if there might just be some technicality in how you are entering your answer. Are you following the instructions exactly? (E.g. whether to include the C)

 

[lookagain]

I think your work is this:

\(\displaystyle \displaystyle \int \frac{4 \ dx}{x\ ln(5x)} = 4 \int \frac{du}{u} = 4 ln(u) = . . . \)

\(\displaystyle \displaystyle 4 \int \dfrac{du}{u} \ = \ 4 ln|u| \ \) + C

 

[Dr.Peterson]

\(\displaystyle \displaystyle 4 \int \dfrac{du}{u} \ = \ 4 ln|u| \ \) + C

Good point. Sometimes we can ignore the absolute value (as in a definite integral), but here we can't, as we don't know the sign of x in an indefinite integral.

jamiecooks1232, are you familiar with this fact? It is almost certainly what your software is complaining about. It would be nice if it could make a comment directing you that way.