A community for students.
Here's the question you clicked on:
 0 viewing
Jonask
 2 years ago
nth integral
Jonask
 2 years ago
nth integral

This Question is Closed

Jonask
 2 years ago
Best ResponseYou've already chosen the best response.2Let \[I_n=\huge\int \frac{x^n}{\sqrt{x^2+a}}\] \[n \in N,a>0,and \space I_n=(a,\infty)\]

Jonask
 2 years ago
Best ResponseYou've already chosen the best response.2I did the first two but three i dont understand

Jonask
 2 years ago
Best ResponseYou've already chosen the best response.2actually it says show that \[I_n=\frac{1}{n}x^{n1}\sqrt{x^2+a}\frac{n1}{n}aI_{n2}\]

Jonask
 2 years ago
Best ResponseYou've already chosen the best response.2\[I_0=\ln(x+\sqrt{x^2+a})\ln\sqrt{a}+c,I_1=\frac{1}{2}\sqrt{x^2+a}+c\]

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.0tried integrating by parts ?

Jonask
 2 years ago
Best ResponseYou've already chosen the best response.2yes\[ f=x^n,f'=nx^{n1}\] \[g'=\frac{1}{\sqrt{x^2+a}}.g=I_0\] \[I_n=x^n(I_0)\int I_0nx^{n1}\]

Jonask
 2 years ago
Best ResponseYou've already chosen the best response.2\[I_n=x^n\ln(x+\sqrt{x^2+a})n\int x^{n1}\ln(x+\sqrt{x^2+a})\]

Jonask
 2 years ago
Best ResponseYou've already chosen the best response.2using parts twice \[\int(x^{n1})\ln(x+\sqrt{x^2+a)}\] \[f=x^n1,f'=(n1)x^{n2}\] \[g'=\ln(x+\sqrt{x^2+a)}\] not sure wat to use for g

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.0let me try lil bit different, \(I_n=\huge\int \frac{x^n}{\sqrt{x^2+a}}dx=\huge\int \frac{x.x^{n1}}{\sqrt{x^2+a}}dx\) now let f(x) = x^{n1} , g'(x) =x/(...)

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.0just a thought, donno whether it'll be useful

Jonask
 2 years ago
Best ResponseYou've already chosen the best response.2thanks it works very well,i tried it,just too lazy to post

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.0oh, it works...good to hear :)
Ask your own question
Sign UpFind more explanations on OpenStudy
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.