If you rewrite numerator as x^4+1-1. Then break up into to fractions (x^4 -1)/(x^2+1) +1/(x^2+1). Second fraction is simply arctan(x) when integrated. First fraction factors as diff of squares into (x^2-1)*(x^2+1) /(x^2+1)=x^2-1. When integrated that gets you (x^3)/3 - x. Therefore the final answer is: (x^3)/3 - x + arctan(x)

Using long division you obtain: x^2 - 1 - 1/x^2 + 1. You then integrate, remember that 1/x^2 + 1 is arctan. 1/3x^3 - x - arctan(x) +C

@moeberry8226

Жыл бұрын

It’s +arctan(x) not -arctan(x).

@amanielmeharena3885

Жыл бұрын

Can you explain why 1/x²+1 is arctan(x)?

@moeberry8226

Жыл бұрын

@@amanielmeharena3885 1/(x^2+1) is not arctan(x), THE INTEGRAL OF 1/(x^2+1) is arctan(x). Because if you differentiate arctan(x) you obtain 1/(x^2+1).

@elimhorn3308

Жыл бұрын

@@amanielmeharena3885 it’s the integral of arctan x, and that’s just the formula.

Just add and subtract 1 in the numerator then the question will be like x^4 +1 -1/x^2+1 then (x^2)2-(1)^2 +1/x^2+1 now (x^2+1)( x^2-1 ) /x^2+1 + int 1/x^2+1dx so by eliminating x^2+1 we get int x^2-1dx + int 1/x^2+1 dx so it will be 1/3 x^3 + tan-1x + c as int of tan-1x =1/1+x^2

Add and subtract 1 on the numerator and break into 2 fractions ,use the difference of squares on the x^4 -1 and so on

Do a trig sub. Set X = tan ø in the numerator it's pretty big tan ⁴ ø but in the denominator it becomes tan squared plus one, this turns to sec ²ø and that cancels out because of the derivative of tan in the numerator. In the end, you split into 2 tan²ø, use the sec identity, one u sub later you get 1/3x³ - X + tan-¹ X + c. Had a feeling there would be an arctan in the answer because thr derivative x² +1 is in the denominator.

Long division also

looks like one of those trig sub integrals

@AJ-er9my

Жыл бұрын

for tangent

X^2+1=(square root x^2+1)^2 then I would use trigonometric subs

Easy integral, use x = tanthetha, and it becomes integral of tan^4theta and aplitting it up we get an answer of x^3/3-x+arctanx

Use the method where you multiply by one.

us a trig substitution?

Use binomial theorem to integrate that 😎

Just use eucliden divison you will x^2-1+1/x^2+1 dx which by distribution of dx you ll get x^3/3-x +arc tan (x) + cste

just do + and - 1 in numerator

nice

But there was no "dx" at the beginning. So you can't do it. Am I right? I dunno man, im still in 11th grade.

Plz write dx in question

@mathscribbles

Жыл бұрын

Yes, that was a typo - sorry for not being perfect ☺️

@elimhorn3308

Жыл бұрын

@@mathscribbles you don’t have to be so passive aggressive, but you should definitely put an equal sign between du/2x and dx.

@mathscribbles

Жыл бұрын

@@elimhorn3308 was not trying to be passive aggressive at all! I acknowledged the typo and that I'm not perfect. 🤗

Add and subtract x² in the numerator, so you can have x²-x²/(x²+1) Than again getting x²-1+1/(x²+1) And this one is easy to integrate

@colinjava8447

Жыл бұрын

Yeah I got the same thing, I think the last bit is tan^-1(x) when integrated

@dwrchschr

Жыл бұрын

@@colinjava8447 it is!

@Lil_shrimp4

Жыл бұрын

Yeah add and subtract one to the top factorise cancel and split the integral

3/2-1 + 1

What kind of computer are y you using for that sir? I’m a physics student looking to get me one and shopping around right now.

@mathscribbles

Жыл бұрын

This is an iPad and using the Goodnotes app. Highly recommend!

@michaeldominguezjr7503

Жыл бұрын

@@mathscribbles thanks for the quick reply my man. I’m gonna go look now! 👍🏾

Hey, can anyone tell me what's going on here? Because i do not understand calculus yet maybe because I'm a freshman in highschool although I'm really intrigued by mathematics yet so far off from my grasp. So if anyone could explain to me in a way that I can understand then good job you would be an A star teacher

Partiallllll fraction

@edizedomat1135

Жыл бұрын

Nope, you can not do it like that

Long division😩

As someone who is pursuing a degree in mathematics, the lack of dx viscerally upsets me

Trig sub this one

U = x^2 its arctan 😂