fizika>

[the_jackal]

Može li netko riješiti ove funkcije:
y = √ (tan (x))

Pokušao sam ovaj koristeći Matlab, ali nisam zadovoljan sam dobio rješenje.

Hvala

 

[kennyg]

y = √ tanx
y ˛ = tanx
2ydy = (sec x ˛) dx = (1 tan x ˛) dx = (1 y ^ 4) dx
dx = 2ydy / 1 y ^ 4,
tako ∫ √ tanx dx = ∫ y 2ydy / 1 y ^ 4 = ∫ (2y ˛ / 1 y ^ 4) dy
= ∫ [(y ˛ 1) / 1 y ^ 4] ∫ dy [(y ˛ -1) / 1 y ^ 4] Dy
= ∫ [(1 y ˝) / (y y ˝ ˛)] ∫ dy [(1-y ˝) / (y y ˝ ˛)] Dy
= A B

:
Let t = y-1 / y, DT = (1 y ˝) dy
i ˝ y y = t ˛ ˛ 2
∫ = 1 / (2 t ˛) dt = 1 / √ 2tan-1 (t / √ 2) = 1 / √ 2tan-1 [(y-1 / y) / √ 2]

B:
Let g = y 1 / y, DG = (1-y ˝) dy
i ˝ y y = g ˛ ˛ -2
∫ B = 1 / (g ˛ -2) = dkg?
I zaboraviti
Posavjetujte račun integracije stol,
naći ćete formulus, a zatim
"A B C konstanta" je rješenje!

 

[elnenez]

<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\frac{-2 tan ^{-1}\left(1-\sqrt{2} \tan ^{\frac{1}{2}}(x)\right) 2 \tan ^{-1}\left(\sqrt{2} tan ^{\frac{1}{2}}(x) 1\right)}{2 \sqrt{2}}' title="3 $ \ frac (-2 tan ^ (-1) \ left (1 - \ sqrt (2) \ tan ^ (\ frac (1) (2)) (x) \ right) 2 \ tan ^ (-1 ) \ left (\ sqrt (2) tan ^ (\ frac (1) (2)) (x) 1 \ right)) (2 \ sqrt (2))" alt='3$\frac{-2 tan ^{-1}\left(1-\sqrt{2} \tan ^{\frac{1}{2}}(x)\right) 2 \tan ^{-1}\left(\sqrt{2} tan ^{\frac{1}{2}}(x) 1\right)}{2 \sqrt{2}}' align=absmiddle>

<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$ \frac{\log \left(-tan(x) \sqrt{2} tan ^{\frac{1}{2}}(x)-1\right)-\log \left(tan (x) \sqrt{2} \tan ^{\frac{1}{2}}(x) 1\right)}{2 \sqrt{2}} Constant' title="3 $ \ frac (\ log \ left (-tan (x) \ sqrt (2) tan ^ (\ frac (1) (2)) (x) -1 \ right) - \ log \ left (tan ( x) \ sqrt (2) \ tan ^ (\ frac (1) (2)) (x) 1 \ right)) (2 \ sqrt (2)) Constant" alt='3$ \frac{\log \left(-tan(x) \sqrt{2} tan ^{\frac{1}{2}}(x)-1\right)-\log \left(tan (x) \sqrt{2} \tan ^{\frac{1}{2}}(x) 1\right)}{2 \sqrt{2}} Constant' align=absmiddle>

 

[the_jackal]

Hvala kennyg i elnenez za rješenje.Imam koristi Matlab riješiti ovaj i ja sam uzimajući potpuno drugačiji rješenje.