Someone integrate the square root of tan x

[GoldenBear]

Good luck.

 

[Capn]

1/2*sqrt(tan(x))*cos(x)*sqrt(2)*arccos(cos(x)-sin(x))/(sqrt(cos(x)*sin(x)))-1/2*sqrt(2)*ln(cos(x)+sqrt(2)*sqrt(tan(x))*cos(x)+sin(x))

Took me 30 seconds

 

[bobachad]

square root of tan x = tanx ^ (1/2)

Dx [Tan x ^ (1/2)] = (1/2) * [Tan x ^ (-1/2)] * (Sec^2 T)

 

[brxndxn]

Well I entered it into the ol' TI 89... We'll see how long it takes..

 

[Angrymarshmello]

<< square root of tan x = tanx ^ (1/2)

Dx [Tan x ^ (1/2)] = (1/2) * [Tan x ^ (-1/2)] * (Sec^2 T) >>



Correct me if I'm wrong (it's been 2 years since Calc 1471 & 1472) but we're taking the integral - so you add 1 to (1/2) instead of subtracting - subtracting is finding the derivative.

My rusty brain got:

(2/3) * (tan x) ^ (3/2) * (anti-derivative of tan x, whatever the h3ll it is)

 

[Capn]

boba, he said integrate, not differentiate.

Doing this kind of thing by hand is pretty useless in the long run, but it's good to learn the basics.

 

[GoldenBear]

<< 1/2*sqrt(tan(x))*cos(x)*sqrt(2)*arccos(cos(x)-sin(x))/(sqrt(cos(x)*sin(x)))-1/2*sqrt(2)*ln(cos(x)+sqrt(2)*sqrt(tan(x))*cos(x)+sin(x))

Took me 30 seconds >>

Actual Answer (I hope)

My ti-89 took about 1 minute (!) to do this, and it gave a long ass answer, longer than the one above it appears. Most integrals take about 2 seconds MAX.

A minimal explanation would be nice too, as I'm hoping there's a pattern here or something..

 

[Capn]

"A minimal explanation would be nice too "

Sure, it's called having a symbolic math package, vis a vis Maple.

 

[GoldenBear]

<< "A minimal explanation would be nice too "

Sure, it's called having a symbolic math package, vis a vis Maple. >>

OMG more details please.

 

[GoldenBear]

Someone here is a geeenius.

 

[j0lly]

Maple is awesome.