!!! CALCULUS!!! ><

lol coming to 4chan... the internet hate machine is definately my last resort... but please some one HELP ME WITH THIS CALCULUS PROBLEMMM AHHHHHH

THE POWER LEVEL OF THIS EQUATION IS OVER 9000!!!!

I CAN'T FIND THE INDEFINITE INTEGRAL OF THIS EQ.

         ...(1-(x)^(1/2))/(1+x^(1/2))

I tried substitution but my equation got only more complicated....

some anonymous mathmeticians/scientists.... one please help... thanks

the internet hate machine
OVER 9000
!!!!
This is not /b/.
Ask as if you weren't a brain-damaged moron and you might get some help.

(1-(x)^(1/2))/(1+x^(1/2))
(-x-1)/(x-1)
done in 30 seconds you fucking moron

I doubt you >>3

>>3
I am asking for the indefinate integral... you have failed. >:[[]]

okay anyways seriously...

I have managed to progress further by manipulating the substitution equation...
u=1 + x^(1/2)
and resulted with
u - 1 = x^(1/2)

When I sub in u-1 for x^(1/2) 
I get (2 - u) / u

Integrating this I get 2ln(u) - u and even after substituting u =
1+x^(1/2) I still don't get the text book's answer

 (5 + 4(x)^(1/2) - x - 4ln(1+ (x)^(1/2)) + C) but this instead...

2ln(1+ (x)^(1/2)) + 1+ (x)^(1/2)

Please help me anonymous mathmeticians/scientists

>>5
1+x^(1/2) != 0
x^(1/2) != -1
x^(1/2)^2 != (-1)^2
x != (-1)^2
x != 1

or from what I answered earlier

x-1 != 0
x != 1

sorry I thought indefinite integral was something else, but still easy
y=(-x-1)/(x-1)
y=(-2)/(x-1)-1
y-1=(-2)/(x-1)
(y-1)/(-2) = 1/(x-1)
(-2)/(y-1) = x-1

(-2)/(y-1)+1 = x

u = 1 + sqrt(x)
du = 1/[2sqrt(x)]dx
sqrt(x) = u - 1, 2sqrt(x) = 2u - 2

du = 1/(2u - 2) dx
dx = (2u - 2) du

so the integral becomes

[1 - sqrt(x)]/u * (2u - u) du

1 - sqrt(x) = -u + 2

(-u + 2) (2u - u) / u du

FOIL the top, divide each term by u, integrate each term seperately

That last part should be:


[1 - sqrt(x)]/u * (2u - 2) du

1 - sqrt(x) = -u + 2

(-u + 2) (2u - 2) / u du

>>7 &
>>8

No idea what you're doing...

>>9
Thats exactly right...
I got the answer! sweet thanks anonymous mathmeticians/scientists....

EPIC WIN!

BTW is 10 ... i think you didn't see 9... lol

Again thanks :)

(%i1) integrate((1-(x)^(1/2))/(1+x^(1/2)), x);
(%o1) 2*(-(x-4*sqrt(x))/2-2*log(sqrt(x)+1))
(%i2) ratsimp(%);
(%o2) -x+4*sqrt(x)-4*log(sqrt(x)+1)