integral

[quaint iris]

i need help

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[warm patio]

Take u = ln(9 + x^2).

[quaint iris]

then i will take ln(9+x^2)'s derivative right?

[warm patio]

Yes, since df = f'dx.

[quaint iris]

okay then i find 1/9+x^2 as du , what should i do next (sorry i am bad at math if i m asking too much questions)

[warm patio]

That's not correct.
First, you didn't take the derivative of ln(9 + x^2) correctly.
Second, you forgot dx.

[quaint iris]

oh so derivative of ln(x) isnt 1/x?

and yeah i forgot dx

oh i forgot the chain rule give me a sec

[quaint iris]

du = 2x/9+x^2 dx

[warm patio]

That's correct.
So, ln(9 + x^2) = u, xdx/(9 + x^2) = (1/2)du. Substitute those into the integral.

[quaint iris]

i dont know if i did it right but i found Xu(9+x^2)du/(9+x^2)(2x)

[warm patio]

Well, which is (1/2)udu.

Which is now easy to integrate.

[quaint iris]

so i did wrong right?

so right one was (1/2)udu

[warm patio]

You just didn't cancel what could be cancelled.

[quaint iris]

oh okayy

[broken tendon]

I wouldve set u to 9+x², so that the x on top and the derivative of u cancel out

Wait then you have to integrate ln(u) whoops

[warm patio]

Well, you'd have to integrate ln(u)/u. So, you would need to make another substitution.

[broken tendon]

I got that this derivative equals ||u²||, is this correct ?

[warm patio]

What derivative?

[broken tendon]

Bzhwhsbbwbs
Integral*

[warm patio]

Oh. Then no.

[quaint iris]

can anyone maybe do it on paper i m still struggling :/

[warm patio]

Well, you have the integral of (1/2)u du. It's just an integral of a power function.

[quaint iris]

yes

and if i want to integrate it, is it (1/2 ) u^2/2 du?

[warm patio]

When you integrate, the differential should disappear. Other than that, yes, you do get (1/4)u^2 + C.

[broken tendon]

I literally can't multiply fractions wow
(1/2)*(1/2)=1/4 not 1
So it's ||u²/4|| ?

No wait it's ||(ln(9+x²)²/4 + c||

[warm patio]

That's correct.