Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing

This Question is Closed

badreferences Group TitleBest ResponseYou've already chosen the best response.1
Now, I'm pretty sure\[u=\ln x\]\[1=\frac{dx}{du}\frac{1}{x}\]\[dx=x\,du=e^{\ln x}\,du=e^u\,du\]\[\int\frac{e^u}{u}\,du\]And I could swear that this can be expressed as some disgusting power series variant.
 2 years ago

badreferences Group TitleBest ResponseYou've already chosen the best response.1
\[\int\left(\frac{1}{u}e^u\right)\,du=\int\left(\frac{1}{u}\sum_{n=1}^\infty u^n\right)\,du\]
 2 years ago

badreferences Group TitleBest ResponseYou've already chosen the best response.1
@Zarkon Check this out please. :3
 2 years ago

badreferences Group TitleBest ResponseYou've already chosen the best response.1
\[\int\sum_{n=1}^\infty u^{n1}\,du\]
 2 years ago

badreferences Group TitleBest ResponseYou've already chosen the best response.1
Whoops, forgot something!
 2 years ago

Zarkon Group TitleBest ResponseYou've already chosen the best response.2
there is no antiderivative in terms of elementary functions
 2 years ago

badreferences Group TitleBest ResponseYou've already chosen the best response.1
Expressing the answer in terms of a sum would be fine.
 2 years ago

badreferences Group TitleBest ResponseYou've already chosen the best response.1
\[\int\frac{1}{u}e^u\,du=\int\frac{1}{u}\sum_{n=1}^\infty\frac{u^n}{n!}\,du=\int\sum_{n=1}^\infty\frac{u^{n1}}{n!}\,du=\sum_{n=1}^\infty\frac{u^n}{n\cdot n!}\]
 2 years ago

badreferences Group TitleBest ResponseYou've already chosen the best response.1
@FoolForMath :D
 2 years ago

badreferences Group TitleBest ResponseYou've already chosen the best response.1
\[\sum_{n=1}^\infty\frac{u^n}{n\cdot n!}=\sum_{n=1}^\infty\frac{\ln(x)^n}{n\cdot n!}\]
 2 years ago

badreferences Group TitleBest ResponseYou've already chosen the best response.1
Can it be further simplified?
 2 years ago

badreferences Group TitleBest ResponseYou've already chosen the best response.1
A better question: what does\[\sum_{n=1}^\infty\frac{\ln(x)^n}{n\cdot n!}\]converge to?
 2 years ago

badreferences Group TitleBest ResponseYou've already chosen the best response.1
By the ratio test it converges.
 2 years ago

Zarkon Group TitleBest ResponseYou've already chosen the best response.2
you should include your constant of integration along with the radious of convergence.
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.0
just a correction :\[\int \frac{1}{u} \sum_{n=0}^{\infty} \frac{u^n}{n!} du=\int (\frac{1}{u}+\sum_{n=1}^{\infty} \frac{u^{n1}}{n!})\ du=\ln u+\sum_{n=1}^{\infty} \frac{u^{n}}{n.n!}+C\]
 2 years ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.