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Dido525Best ResponseYou've already chosen the best response.1
How the heck did wolfram jump from the first step to the second step? I feel like I am missing something.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
It's the second step I am not getting.
 one year ago

Dido525Best 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.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
THe picture I posted is near the final answer.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
I see no other way to solve it.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Eww... More partial fractions?
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
But we only have 1 term divedby a polynomial . You have to use partial fractions.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Partial fractions do not help at all. You can't reduce this.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Allright. 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.
 one year ago

sirm3dBest ResponseYou've already chosen the best response.2
\[\Large \sqrt{x^22x+5}=\sqrt{(x1)^2 + 4}\] use trigonometric substitution \[\Large x1=2\tan \theta\]
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
@sirm3d : Okay why did you square root?
 one year ago

sirm3dBest ResponseYou've already chosen the best response.2
oh, sorry, it was squared. the partial fraction is \[\frac{x}{(x^22x+5)^2}=\frac{Ax+B}{x^22x+5}+\frac{Cx+D}{(x^22x+5)^2}\]
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
So it's actually possible to split this up? O_o .
 one year ago

sirm3dBest ResponseYou've already chosen the best response.2
i see that, too. \[x=(1/2)(2x)=(1/2)(2x2+2)=(1/2)(2x2) + (1/2)(2)\]
 one year ago

sirm3dBest 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 \[x1=2\tan\theta\]
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
So now I have: \[\int\limits_{}^{}\frac{ 1 }{ (x^22x+5)^2 }dx\]
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
But we have a and b are 0 so the first term is entirely 0.
 one year ago

sirm3dBest ResponseYou've already chosen the best response.2
i realized that too, partial fraction doesn't work. check my previous post.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
\[x=Ax^32Ax^2+Bx^22Bx+Cx+5B+D\]
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
x1=2tan(theta) dx=2sec^2(theta) d(theta)
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
\[\int\limits\limits_{}^{}\frac{ 1 }{ u^2 } du+ \int\limits\limits_{}^{}\frac{ 4\sec^2 \theta }{ 2(4\sec^2\theta) }d \theta\]
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
I get that which doesn't seem right...
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
I used u instead of y.
 one year ago

sirm3dBest ResponseYou've already chosen the best response.2
\[x1=2\tan\theta\\x^22x+5=4\sec^2\theta\] \[\large (1/2)\int \frac{du}{u^2}+\int\frac{2\sec^2 \theta d\theta}{(2\sec \theta)^4}\]
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
\[x1=2\tan\theta\] \[dx=2\sec ^2\theta d \theta\]
 one year ago

sirm3dBest ResponseYou've already chosen the best response.2
yes. our numerators agree.
 one year ago

sirm3dBest ResponseYou've already chosen the best response.2
@amistre64 , can you take over? i have to catch some sleep.
 one year ago
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