Integrate: (tan x)^0.5
2006-09-11 05:56:48 · 5 answers · asked by Mihir Durve 3 in Science & Mathematics ➔ Mathematics
Try the substitution
u = tan x
x = arctan u
dx = du/ (u^2 + 1)
Then it becomes
int ( u^0.5 du/ (u^2 + 1) )
Now let's make another substitution:
t = u^0.5, u = t^2, du = 2t dt
Then we have to integrate
2t^2 dt/(t^4 + 1),
a rational function!
So, let's use the method of partial fractions.
First, we must factor the denominator.
Note that
t^4 + 1 = t^4 + 2t^2 +1 - 2t^2
=( t^2 + sqrt(2)t +1)(t^2 - sqrt(2)t +1)
So the partial fractions decomposition looks like
(at + b)/(t^2 + sqrt(2)t +1) + (ct + d)/(t^2 - sqrt(2)t +1).
I'll let you carry on from here.
You can check your work at integrals.wolfram.com
Good luck!
2006-09-11 07:24:30 · answer #1 · answered by steiner1745 7 · 0⤊ 0⤋
This is fairly complecated and you can see the link
2006-09-11 07:06:15 · answer #2 · answered by Mein Hoon Na 7 · 0⤊ 0⤋
The result is pretty complex
http://img45.imageshack.us/img45/2171/clipboard1fb6.png
2006-09-11 06:42:06 · answer #3 · answered by Keex 2 · 0⤊ 0⤋
cosine of the sine of 5.0
2006-09-11 06:00:00 · answer #4 · answered by David G 3 · 0⤊ 1⤋
what
2006-09-11 06:01:42 · answer #5 · answered by sunshine girl 3 · 0⤊ 2⤋