#could someone help me with this integral?
abstract tapir
ashen ventureBOT
stone atlas
could always use partial fractions if ur bothered
thick wagon
Partial fraction won’t tly work fr
stone atlas
Partial fraction won’t tly work fr
why?
the other option is to complete the square
it seems
thick wagon
Cause they are both the same thing
stone atlas
Cause they are both the same thing
if u have partial fractions u can just integrate each component separately cant u?
thick wagon
if u have partial fractions u can just integrate each component separately cant ...
Yes…
But the denominator is the same
A/(x^2+x+1)+b/(x^2+x+1)
stone atlas
partial fractions
stone atlas
whoops, i was being silly
stone atlas
i forgot 1/(A+B) cant be turned into 1/C +1/D
thick wagon
stone atlas
So, how would one use complete the square
u can get somethjing that looks like a trig thingy
after a usub
thick wagon
Ah
stone atlas
very pretty
thick wagon
The arc tan pray thing
stone atlas
1?
thick wagon
$\int \frac{dx}{x^2+x +1}$
bold ridgeBOT
axkyn
thick wagon
3/4 and 1/4
thick wagon
(X+1/2)^2
stone atlas
my favourite completing the square ahhaha
stone atlas
u need to take out all the fractions
thick wagon
$\int \frac{dx}{((x+\frac{1}{2})^2 \frac{3}{4}}$
stone atlas
take out a factor of half from the bracket -> 1/4 -? 16 outside
bold ridgeBOT
axkyn
thick wagon
My latex ass gimme a few
stone atlas
its okay i cant latex at all xd
also i think i will slepe
goood luck to tasakman95
steel crown
cant you just calculate int(1/(x²+x+a))dx and then do leibniz rule?
stone atlas
cant you just calculate int(1/(x²+x+a))dx and then do leibniz rule?
thats not an easy integral either?
steel crown
wellll
stone atlas
cant you just calculate int(1/(x²+x+a))dx and then do leibniz rule?
wait i dont understand how you could use leibniz here
steel crown
d/da
stone atlas
but why would that make it easier
steel crown
because this int(1/(x²+x+a))dx isnt that hard
stone atlas
but its fundamentally the same as the other
thick wagon
cant you just calculate int(1/(x²+x+a))dx and then do leibniz rule?
Can you make it a limit
The answer is no ; )
steel crown
wdym?
thick wagon
An integral is not a limit
steel crown
ik
vernal crane
$\int \frac{d!x}{((x+\frac{1}{2})^2+\frac{3}{4}}$
There was meant to be a plus
bold ridgeBOT
∫(∂∑)ω=∫(∑)dω
vernal crane
You can just do $x+\frac{1}{2}$=$\frac{\sqrt{3}}{2}\cos(u)$
bold ridgeBOT
∫(∂∑)ω=∫(∑)dω
thick wagon
$\int \frac{d\!x}{((x+\frac{1}{2})^2+\frac{3}{4}}$
There was meant to be a plus
Yes I know
thick wagon
It’s arc tan I thought
vernal crane
oh wait i am tripping
abstract tapir
**∫(∂∑)ω=∫(∑)dω**
if it was smth like that i would have solved it but i dont know since it is to the seceond power
(sry for my english im from poland)
vernal crane
So $x+\frac{1}{2}=\frac{\sqrt{3}}{2}\tan(u)$ and $d!x=\frac{\sqrt{3}}{2}\sec^2ud!u$.
And then it becomes $\frac{8\sqrt{3}}{9}\int\frac{\sec^2ud!u}{\sec^4u}$
hopefully
bold ridgeBOT
∫(∂∑)ω=∫(∑)dω
vernal crane
and $\int\cos^2(u)d!u$
bold ridgeBOT
∫(∂∑)ω=∫(∑)dω
steel crown
dont you just do u= x+ 1/2 and du=dx to make it int(1/(u²+((sqrt(3))/2))dx to then use int(1/(x²+a²)dx=1/a arctan(x/a) ?
steel crown
dont you just do u= x+ 1/2 and du=dx to make it int(1/(u²+((sqrt(3))/2))dx to th...
+C ._.
vernal crane
dont you just do u= x+ 1/2 and du=dx to make it int(1/(u²+((sqrt(3))/2))dx to th...
its more of a int (1/(x^2+a^2))^2dx type of thing
steel crown
its more of a int (1/(x^2+a^2))^2dx type of thing
just use leibniz to get that
obsidian raptor
Brute force it
vernal crane
ye
