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Someone integrate the square root of tan x

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
 


<< 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)
 
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.
 


<< 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..
 
"A minimal explanation would be nice too "

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


<< "A minimal explanation would be nice too "

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

OMG more details please.
 
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