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/sci/ - Science & Math

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3945343 No.3945343 [Reply] [Original]

Fuck how does change of variables work again for integrals

eg. int x*(x-3)^2 let u = x-3;
u+3 * (u)^2

= u^3 + 3u^2
= u^4/4 + u^3 = (x-3)^4 + (x-3)^3. But that doesnt equate when you factor the whole thing out and integrate.

Wolfram says that they're equivalent for restricted x or something. Anyone help me out RQ?

>> No.3945348

Fuck why do you always post the same fucking pictures?

>> No.3945349

honestly op I would just foil it and distribute the x then integrate it. you're making it harder than it needs to be.

>> No.3945352

>>3945349
not to mention I have no idea what you're doing with your math it's (u+3)*(u^2) not u + 3u^2 or whatever it is you're doing

>> No.3945359

>>3945352
strike that I see you just didn't write a step. let me check it out

>> No.3945378

>>3945359
no idea, now im curious too.

>> No.3945400

anyone know?

The restricted values of x that WA gives is the solution you get when you integrate without substituting, that's probably part of it.

>> No.3945409

Why dont you just expand (x-3)^2 and multiply each term by x?
integrating polynomials is easier

>> No.3945428

>>3945409
I think he just wants to know why it's not the same when you integrate like how you said.

>> No.3945429

>>3945343
>= u^3 + 3u^2
>= u^4/4 + u^3

u^4/4????? what is this?

you can integrate here:
= u^3 + 3u^2

>> No.3945438

>>3945429
his integration is correct although incorrectly written he meant to put (u^4)/4