I need help urgently with this.

[hollow idol]

pls help

[versed shoal]

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[hollow idol]

$\int_0^1 \left( \frac{x^2 + 2x + 1}{(x^3 + 3x^2 + 3x + 1)^2} \right) dx + \frac{d}{dx} \left( e^{x^2} \cdot \sin(x) \right) + \lim_{n \to \infty} \sum_{k=1}^{n} \frac{1}{k^2}$

[frosty cave]

doodle

[hollow idol]

Find the value of the integral, derivative, and limit.

[neat moon]

you can do some factoring for the integral

[hollow idol]

how so

im in 10th grade

[neat moon]

how are you doing calc then

uhh

do you know binomial expansion of (a+b)^3

[hollow idol]

idk 😭

[lavish token]

The limit is the famous Bass n’ Ale problem and it is equal to 6/e^2.

The derivative can be done easily by hand by applying the product rule and chain rule, but logarithm differentiation is always an option.

The integral is just a u substitution, it’s extremely easy once you spot it

[hollow idol]

no

[lavish token]

Your teacher has no originality or sense of style whatsoever

[neat moon]

lmao

[hollow idol]

how so

[lavish token]

He literally just computed the derivative of a simple function and then slapped that down there

[hollow idol]

whats a derivative bro

[lavish token]

Alright bro how are you presenting this to your teacher

Can you email him?

[hollow idol]

idk im js gonna give him the answer that u say

xd

im in 10th grade

[shut linden]

489

[hollow idol]

ok

[shut linden]

💀

dont

@hollow idol

[hollow idol]

ok bruh

chatgpt said

$Here are the summarized results for the given expression:

1. Integral:

\int_0^1 \left( \frac{x^2 + 2x + 1}{(x^3 + 3x^2 + 3x + 1)^2} \right) dx = \frac{7}{24}

2. Derivative:

\frac{d}{dx} \left( e^{x^2} \cdot \sin(x) \right) = (2x \sin(x) + \cos(x)) e^{x^2}

3. Limit:

\lim_{n \to \infty} \sum_{k=1}^{n} \frac{1}{k^2} = \frac{\pi^2}{6}$

[lavish token]

Email them something like “The limit is the famous Basel problem and it is equal to pi^2/6 due to Euler. The derivative, which can be computed via the chain rule and product rule is just 2xe^(x^2) sin(x) + e^(x^2) cos(x). The integral, lacking in originality, directly follows from a u substituion and is 7/24.”

[neat moon]

do not just chatgpt for math smh

[lavish token]

ChatGPT is garbage

Ignore it

[hollow idol]

ok

[lavish token]

tell them people on the internet call them unoriginal and boring

[hollow idol]

so that's just the straight answer?

[hollow idol]

💀

@lavish token 1 question

why are u randomly searching on Google about famous maths equations

are u a maths teacher or college teacher?

[lavish token]

I mean, I don’t do it randomly, these are just things you learn if you study mathematics

The Basel problem result is famous

[hollow idol]

alr zawglus ima email him the answer u gave mr

and i get an easy 5$

[lavish token]

he better pay up

[winged yoke]

$\int_{0}^{1} \frac{1}{(x+1)^4} dx+ 2xe^{x^2}\sin(x)+e^{x^2}cos(x)+\frac{\pi^2}{6}$

[frosty cave]

;( | 追放された興奮

[hollow idol]

bye bye 🤫 🧏

$close

ok.

[neat moon]

+close