/sci/ - Science & Math

[Anonymous No.8544156]

>today
>to intelligent two study
>pic related in exam
>easy as fuck
>got confused by INT(x-1)^-2
>1h30min trying the fucking problem with integ. methods and log shit
>5 min left
>I remembered the denominators method exist
>check answer online
>(x-1)^-1
>tfw there were another question left
>tfw I might get up to 6/10 because of this problem
R*E^(10^100)

[Anonymous No.8544175]

>1h30min trying the fucking problem with integ. methods and log shit
Didn't even try a u sub? Or think about moving on to the next question?

[Anonymous No.8544251]

Please tell me those polynomial are irreducible

[Anonymous No.8544261]

>>8544251

Can group the denominator up and haul our -X^2 on the left. Too intellectual to do it fully tb.h

[/A/nonymous !cPUZU5OGFs No.8544304]

>>8544156
[math]\frac{2x^2+x+3}{x^3-x^2-x+1} = \frac{2x^2+x+3}{(x+1)(x-1)^2}\\
\frac{2x^2+x+3}{(x+1)(x-1)^2} = \frac{A_0}{x+1}+\frac{A_1}{x-1}+\frac{A_2}{(x-1)^2}\\
2x^2+x+3 = A_0(x-1)^2+A_1(x-1)(x+1)+A_2(x+1)\\
2x^2+x+3 = A_0(x-1)^2+A_1(x^2-1)+A_2(x+1)\\
\left\{ \begin{array}{ccc}
x=+1 & 2+1+3 = 2A_2 \\
x=-1 & 2-1+3 = 4A_0 \end{array} \right.\\
\left\{ \begin{array}{ccc}
x=+1 & 6 = 2A_2 \\
x=-1 & 4 = 4A_0 \end{array} \right.\\
\left\{ \begin{array}{ccc}
x=+1 & 3 = A_2 \\
x=-1 & 1 = A_0 \end{array} \right.\\
x=0 \hspace{4 mm} 0+0+3 = A_0 -A_1 + A_2\\
x=0 \hspace{4 mm} 3 = 1 -A_1 + 3\\
x=0 \hspace{4 mm} -1 = -A_1\\
x=0 \hspace{4 mm} A_1 = 1\\
\frac{2x^2+x+3}{(x+1)(x-1)^2} = \frac{1}{x+1}+\frac{1}{x-1}+\frac{3}{(x-1)^2}\\
\int \frac{1}{x+1}\,dx + \int \frac{1}{x-1}\,dx + \int \frac{3}{(x-1)^2}\,dx\\
ln(x+1) + ln(x-1) + \int \frac{3}{u^2}\,du ; \hspace{4 mm} u=x+1, dx=du\\
ln(x+1) + ln(x-1) + \frac{3}{u}\frac{1}{-1} + C\\
ln(x+1) + ln(x-1) - \frac{3}{x+1} + C\\
[/math]

[Anonymous No.8544318]

>>8544251
>cubic
>irreducible

[/A/nonymous !cPUZU5OGFs No.8544321]

>>8544304
[math]u=x-1,dx=du\\
ln(|x^2-1|)-\frac{3}{x-1}+C[/math]

[Anonymous No.8544387]

>>8544175
>tfw to intelligent two skip questions

[Anonymous No.8544399]

>>8544156
Because most physics is dull

[Anonymous No.8544404]

>>8544304
Did you do that first factorization by inspection? I totally missed that

[OP No.8544430]

>>8544304
Literally me.

I still feel a lot of anger tonight. How the fuck do I get rid of this inner screeching?

[Anonymous No.8544447]

>>8544404
https://en.wikipedia.org/wiki/Rational_root_theorem
It really helps to quickly find the roots.

[/A/nonymous !cPUZU5OGFs No.8544782]

>>8544404
>>8544447
It was Inspection. Thanks for the Rational Root theorem.

[Anonymous No.8545078]

>>8544304
in the first step doesn't the last fraction have to be A2x+A3 over (x-1)^2 because youre dividing by a nonlinear function?

[Anonymous No.8545190]

>>8545078
Nope, that's only in the case of an irreducible quadratic. That is (x-1)(x-1)

[Anonymous No.8545306]

>>8544156
>didn't study
>got question wrong
>angry

You should now know you aren't as smart as you thought.

Study.

[Anonymous No.8545309]

>>8544156
partial fractions and basic trig substitutions are literally the only things I remember from calc 2

[Anonymous No.8545432]

>>8544156
>>check answer online
what?

[Anonymous No.8545494]

>>8545432
After the exam I checked the answer online.
But I had everythin good.
The only problem was a simple Int[(x-1)^-2]dx

Fucking hell. It was to easy two study tho.

[Anonymous No.8545501]

>>8545494
You should just skip university its for dumb people, just go get a job already. What are you? A brainlet?

[Anonymous No.8545520]

>>8545501
I know, but I think it's a smart decision to do it anyway. Call it a genius' intuition.

[Anonymous No.8547013]

>>8545306

This.

Also applies to this entire board.

[Anonymous No.8547020]

>Had nearly same question on my final.

>Breezed through it in 5 minutes.


Maybe you should have studied, little baby brainlet.

[Anonymous No.8547045]

>having finals where you compute hard integrals

Disgusting. You will NEVER need to do this by hand again, fyi

[Anonymous No.8547566]

>>8544156
>factorize denominator
>partial fractions
>easy as shit integrals

Literally 5 minutes.

[Anonymous No.8547584]

>>8547020
If you have to study you are a brainlet.

[Anonymous No.8547749]

I gave up on "solving" integrals when I took probability. Now I just take a pair of dice to every "calculus" class and that usually gives me the right answer if I just apply the Monte Carlo method and other actual useful properties of probability.

[Anonymous No.8548050]

>>8544304
Wrong. Did you even check your work with wolfram?

[Anonymous No.8548059]

>>8544156
Just subtract both sides