A community for students.
Here's the question you clicked on:
 0 viewing

This Question is Closed

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1How the heck did wolfram jump from the first step to the second step? I feel like I am missing something.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1It's the second step I am not getting.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1\[\int\limits\limits_{}^{}\frac{ x }{ (x^22x+5)^2 }dx\] I put that intergal into wolfram. Then I put the show steps.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1THe picture I posted is near the final answer.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1I see no other way to solve it.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1Eww... More partial fractions?

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1But we only have 1 term divedby a polynomial . You have to use partial fractions.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1Partial fractions do not help at all. You can't reduce this.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1Allright. It's almost 4:30 AM here. If someone could leave an explanation I would GREATLY appreciate it once I wake up in the morning.

sirm3d
 2 years ago
Best ResponseYou've already chosen the best response.2\[\Large \sqrt{x^22x+5}=\sqrt{(x1)^2 + 4}\] use trigonometric substitution \[\Large x1=2\tan \theta\]

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1@sirm3d : Okay why did you square root?

sirm3d
 2 years ago
Best ResponseYou've already chosen the best response.2oh, sorry, it was squared. the partial fraction is \[\frac{x}{(x^22x+5)^2}=\frac{Ax+B}{x^22x+5}+\frac{Cx+D}{(x^22x+5)^2}\]

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1So it's actually possible to split this up? O_o .

sirm3d
 2 years ago
Best ResponseYou've already chosen the best response.2i see that, too. \[x=(1/2)(2x)=(1/2)(2x2+2)=(1/2)(2x2) + (1/2)(2)\]

sirm3d
 2 years ago
Best ResponseYou've already chosen the best response.2\[\frac{x}{(x^22x+5)^2}=\frac{(1/2)(2x2)}{(x^22x+5)^2}+\frac{(1/2)(2)}{(x^22x+5)^2}\] for the first term, use the substitution \[y=x^22x+5,\quad dy=(2x2)dx\] for the second term, use the trigonometric substitution \[x1=2\tan\theta\]

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1So now I have: \[\int\limits_{}^{}\frac{ 1 }{ (x^22x+5)^2 }dx\]

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1But we have a and b are 0 so the first term is entirely 0.

sirm3d
 2 years ago
Best ResponseYou've already chosen the best response.2i realized that too, partial fraction doesn't work. check my previous post.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1\[x=Ax^32Ax^2+Bx^22Bx+Cx+5B+D\]

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1x1=2tan(theta) dx=2sec^2(theta) d(theta)

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1\[\int\limits\limits_{}^{}\frac{ 1 }{ u^2 } du+ \int\limits\limits_{}^{}\frac{ 4\sec^2 \theta }{ 2(4\sec^2\theta) }d \theta\]

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1I get that which doesn't seem right...

sirm3d
 2 years ago
Best ResponseYou've already chosen the best response.2\[x1=2\tan\theta\\x^22x+5=4\sec^2\theta\] \[\large (1/2)\int \frac{du}{u^2}+\int\frac{2\sec^2 \theta d\theta}{(2\sec \theta)^4}\]

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1\[x1=2\tan\theta\] \[dx=2\sec ^2\theta d \theta\]

sirm3d
 2 years ago
Best ResponseYou've already chosen the best response.2yes. our numerators agree.

sirm3d
 2 years ago
Best ResponseYou've already chosen the best response.2@amistre64 , can you take over? i have to catch some sleep.
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.