Question

help please...
how i integrate this

Answer 1

\[\int\limits_{}^{}\frac{ 1 }{ (x^2+1)^2}\]

Answer 2

@agent0smith

Answer 3

dx*

Answer 4

this one needs a big dose of sharkasm

Answer 5

You could apply the reduction formula.

Answer 6

hmm how .. im lost

Answer 7

go with a tan sub

Answer 8

so how do you know its a tan ? is there like a formula to it ?

Answer 9

\[\int\limits_{?}^{?}(1)/(ax^2 +b)^n dx = (2n - 3)/2b(n-1)\int\limits_{?}^{?}(1)/(ax^2 +b)^n-1) dx + (x)/2b(n-1)(ax^2 +b)^n-1 \]
When a = 1, b = 1, n =2
The -1 after (ax^2 + b) is supposed to be ^n-1, so is the last one.

Answer 10

It's tangent because the denominator has the form (stuff)^2+1.
And we know that our tangent identity has the form (tan)^2+1, yes?

Answer 11

What you have is a standard integral, which equals: arctan(x)

Answer 12

oh okay so then

Answer 13

Let me finish, real quick.

Answer 14

\[1/2 \int\limits_{?}^{?} (1)/(x^2+1) dx + (x)/(2x^2+1) \]
This is what you receive after you apply the reduction formula, but it can be simplified to:
\[\arctan(x)/2 + (x)/2(x^2+1) + C \]
Which can be further simplified as :
\[\arctan(x)/2 + (x)/(2x^2 + 2) + C\]

Answer 15

With the stance of knowledge the integral is standard and equal to arctan(x) for the first part.

Answer 16

What is this formula..? 0_o weird...

Answer 17

My teacher taught it to me, it seems to work, if not then I am not sure. She suggested it.

Answer 18

Weirrrrrd :D lol

Answer 19

It's supposed to help with integration by parts. >.< At least that is what I was told.

Answer 20

So ya.. another way to approach the problem is with trig sub.
\(\large\rm x=\tan\theta\)

Understand how to proceed from there Marci? :d
\(\large\rm dx=?\)

Answer 21

woah lol

Answer 22

sec^2 theta

Answer 23

Oh yeah, in my notes, "any kind of integral has it's own type of reduction formula depending on how it is setup."

Answer 24

oh so what other reduction formulas do you know of @Vuriffy

Answer 25

Every integral I have learned about has a form of reduction formula which corresponds with the values given in the integral. I don't know exactly how to explain it.

Answer 26

ohhh lool

Answer 27

\[\large\rm dx=\sec^2\theta~d \theta\]Yes.
So then plug in the pieces.

Answer 28

\[\large\rm \int\limits\frac{1}{(\color{orangered}{x}^2+1)^2}\color{royalblue}{dx}\quad=\quad\int\limits\frac{1}{(\color{orangered}{?}^2+1)^2}\color{royalblue}{?}\]

Answer 29

tan^2x