integral

[worldly surge]

I need to solve this integral, but I don't understand how to do it.

[valid lance]

what is your progress?

[worldly surge]

None. I don't know how and where to start

[valid lance]

try x = cos theta

@worldly surge

sorry for the late reply

do you know the half angle formulae?

sorry ignore all my work and handwriting

just follow the arrows

i am a little confused what should we do next

did another substitution

It just gets messier after the double substitution

@worldly surge sorry cant do it :(

@minor oracle yo how u do this shi

@frank tulip

[frank tulip]

imma try this when i hit home and honestly a nap

[valid lance]

Alright sir

I'll try again after coming back from my gym

[worldly surge]

it's all good. don't worry

[frank tulip]

are you in university or school?

[random raven]

wtf this is a good problem

nothing is working shit

@worldly surge

brother

are u sure the function is correct

[frank tulip]

relax

[random raven]

yeah i should fr

bro

@frank tulip

could we try

putting x = ln t or something

as there is a derivative

idt trig is really helping

i tried sin cos tan tan^2

nothing fucking works

[worldly surge]

University

[worldly surge]

Yes

[valid lance]

Lmao yeah fr

I did like 3 pages nothing worked

And do not even think of subbing ln x

Why do you wanna make your live a living hell @random raven

[frank tulip]

I also tried various things but didnt come far, the Integral also looks really long and conplicated so I think I wont bother with anymore haha

[valid lance]

Oh nah this shit is way too long

[minor oracle]

Maybe try Xander's way
Sub x = e^t
=> ln(x) = t

That way you can atleast get rid of the 1/x which is outside the cuberoot

[valid lance]

But my way most of it is solved

Can you check my work @minor oracle

CosX = t

[random raven]

valid

[minor oracle]

Don't you think you've made it worse here? 🥲

[low stirrup]

note that $\f{1-x}{1+x}=\f{1+x-2x}{1+x}$

[sand ocean]

🫎 A Certain User(Moosey) 🫎

[minor oracle]

Yes, but where do you go from there?

2x/1+x is still something to solve for

[low stirrup]

u=1+x

albeit that gets you a 1/u, so i still dk

[minor oracle]

Actually. Yes. That's so genius

The splitting allows you to cancel out the external 1/x

Heck yeah

[low stirrup]

...does it?

[minor oracle]

It doess

[low stirrup]

but it becomes 1/(u-1)

[minor oracle]

So, the bracket part gets split to
1 - 2x/1+x

After you multiply the 1/x to these two terms, you get
1/x - 2/1+x

[low stirrup]

oh wait

[minor oracle]

These you can solve now pretty easily ig

[low stirrup]

1/x

becomes 1/x^3

when you move it in the cube root

[minor oracle]

Oh wait, there's a cuberoot

[low stirrup]

lmao

[minor oracle]

I forgor about that 💀

[frank tulip]

se x common

[minor oracle]

Works everytime

You can do that

Let's try that

[low stirrup]

bleak

[frank tulip]

I wonder how people come up with those random integrals lol

"Yeah i just got into calc 1 and my professor gave me this lol help"

[minor oracle]

Bros cook when no one asks them to

[valid lance]

Idk I solved many questions like these and it got solved

[random raven]

ukw

wolfram alpha

😭

frr

[empty urchin]

It says do a u sub for ln x

[random raven]

yeah i did that

but it didnt work

[empty urchin]

Then replace the x with e^u

Then do another u sub with the stuff inside the cbrt

🤷

i wouldn’t have come up with this by myself

[winter sky]

have you tried any online integral calculator?
https://www.integral-calculator.com/

[worldly surge]

i will thankss

[empty urchin]

yea i used this one

[winter sky]

you're welcome 🙂

[valid lance]

Why do intelligent people even exist