Question

Integral Problem:

Answer 1

\[\int\limits_{}^{} 9x/\sqrt{1-81x^4}\]

Answer 2

okk
take x^2=t

Answer 3

2x*dx=dt
x8dx=dt/2

Answer 4

It is multiple choice:

A) (1-9x^2)^1/2 + C
B) 1/2(1-9x^2)^3/2 + C
C) -1/2arcsin(9x^2) + C
D) arcsin(9x^2) + C
E) 1/2arcsin(9x^2) + C

Answer 5

Did you get t=x^2 because you divided the variable because that is the arcsin formula?

Answer 6

How did you get t=x^2?

Answer 7

in ur numerator x is there
so if we have to substitue a variable whose differentiation =x

Answer 8

in numerator x^4
is there
x^4 diff=4x^3
x^3 diff=3x^2
x^2 difff= 2x
so we will take x^2=t

Answer 9

Okay maybe that's my problem.
Why did you take the third derivative?

Answer 10

on differentiation
2x*dx=dt
x*dx=dt
which convert numerator
x*dx into dt
so we left with
int(9/sqrt(1-81*t^2) * dt/2

Answer 11

i was just showing u wat we should take so that after differentiation we get x*dx

Answer 12

if we take x^4=t
on diff
4x^3*dx=dt

Answer 13

if we take x^3=t
on diff
3x^2*dx=dt

Answer 14

Oh because you want to get the x out of the numerator.
Alright I got you.

Answer 15

but we need x*dx
so if we take x62=t
on diff
2x*dx=dt

Answer 16

dx = dt/2x then

Answer 17

no lolll
x*dx=dt/2

Answer 18

Because we have to keep the variables separated? I'm think i'm sort of following.
What is next?

Answer 19

look if we eleminate x from numerator than we will have variable only in denominator

Answer 20

Hey I was doing a little bit of research and maybe the problem is simpler than we thought

Integral(1/(a^2 - x^2)^1/2 = arcsin(x/a) + C

Answer 21

\[\int\limits_{}^{} \frac{ 9*x*dx }{ \sqrt{1-81(x^2)^{2}} }\]

Answer 22

Is this what you were talking about?

a = 1
x = 9x^2

Answer 23

x^2=t
2xdx=dt
xdx=dt/2

Answer 24

replace xdx by dt/2 and x^2 by t

Answer 25

1/2 arcsin(9x^2) + C ?

Answer 26

\[\int\limits_{}^{}\frac{ 9*\frac{ dt }{ 2} }{ \sqrt{1-81(t)^{2}} }\]

Answer 27

Oh because xdx = dt/2, that is where I get the positive 1/2 in the problem

Answer 28

Okay thank you!
The answer is E right?

Answer 29

\[\frac{ 9 }{ 2 }\int\limits_{}^{}\frac{ dt }{ \sqrt{1^{2}-(9t)^{2}}}\]

Answer 30

loll u calculate that ..i dont remember the exact formula

Answer 31

The formula is arcsin(x/a) + C
I looked it up
So you're saying that it's arcsin(9x) + C right?

Answer 32

I'm going to go with E, but thanks anyways

Answer 33

Wait a minute!

Answer 34

Hallelujah!

Answer 35

It's D!

Answer 36

Exactly what you said lol