what substitition do i do here

[forest granite]

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[placid ore]

U can use the property where u can replace x with 1-x

Or try by parts

or take x^2+1=t^2

The third one is the best alternative imo

Basically u wanna convert the root part into one variable

So that u can seperate it

[chrome yoke]

how will i do this, because theres dx

[placid ore]

Dx=dt/2x

When u cancel x^2 by 2x

U get x/2

So x can be root of t^2-1

U should write this down and see where u get

[sterile coral]

i was thinking of trig sub

[placid ore]

That isn't necessary

[sterile coral]

yeah nah probably overkill

[placid ore]

Anyway hi

Mikuroll

;))

[sterile coral]

😄

[chrome yoke]

how do you get dx=dt/2x

from x^2+1 = t^2

[placid ore]

Yeah it should be dx=2tdt/2x

Whatever man u get the point

[chrome yoke]

wait, you can differentiate both sides like that?

[placid ore]

Yes

Ofc

Or just take √[x^2+1]=t

[chrome yoke]

so 2x dx = 2t dt? like that?

[placid ore]

Yes

[chrome yoke]

what is the method after this

t(t^2-1) dx

[placid ore]

Are u sure that's what ur getting

Also it should be dt

Caus if that's it then just distribute and integrate

But i doubt ur doing it right

[chrome yoke]

i got √[x^2+1]=t then
integral becomes x^2 t dx

then i replace t with √[x^2+1] ?

but then i get x^2 √[x^2+1]

[placid ore]

Look

U get t

U have txdt

X =√t^2-1

Simple u sub after that

[chrome yoke]

i get t^2 x dt

dx = 2t/2x dt
then 2 cancel out
dx = t/x dt
x^2 t dx becomes
x^2 t * t/x dt

[placid ore]

1+x^2)^1/2 becomes t

Cancel x^2 with the x in denominator (dx=tdt/2x)

So u have xt^2dt

Converting x in terms of t

U get t^2(t^2-1)^1/2

Hmm

Doesn't help at all

How bout u replace x with 1-x

And try to add and stuff

[chrome yoke]

replace x with 1-x?

[placid ore]

Yes it's a property in definite integrals

Integral of f(x) from 0 to p= f(p-x) from 0 to p

Another try..

Take x^2 common out of root

[sterile coral]

i think tan sub should be good

[placid ore]

So u get x^3*(1+1/x^2)

X^2 =t

[sterile coral]

but im not thinking too hard

[placid ore]

Now u get t*√(1+1/t)dt

Ok doesnt work either

[placid ore]

It might work

Yep it does

Bruh

Fuck u ;)

I tried too hard

And u did it without thinking to hard

Well once u did mention trig sub i thought I must do it without it lol

[sterile coral]

i just do a lot of integrals

it comes with practice

[sterile coral]

that i can relate

[chrome yoke]

thanks guys @placid ore @sterile coral

[knotty cypress]

@chrome yoke has given 1 rep to @strong imp @sterile coral