Integrate the Arcsine Function

[FlashStorm]

integrate the holy arcsine x :(

Homework Statement

The Integral arcsine (x) appears to be really problematic. I have to calculate the integral of sqrt(1-x^2). part of it is the arcsine x.

Now I will ask only about arcsine x, and If any serious problem will occur i'll bother you with the another one :)

Homework Equations

The Attempt at a Solution

I used Integration by parts , which was also suggested by someone on this site and forums (another forums which I accidentally wrote my question there).

S(arcsine x)= {v=x u=arcsine x}
xarcsine-S(x/sqrt(1-x^2)= {u= x v=arcsinx}
S(arcsine x)


What have I done wrong till now? Tried to look for different substitutions but didn't find anything of a value. moreoever, I just recently started studying it so have mercy :P

Thanks in advance,
Aviv

 

[siddharth]

S(arcsine x)= {v=x u=arcsine x}
xarcsine-S(x/sqrt(1-x^2)= {u= x v=arcsinx}
S(arcsine x)

ok, to find $$\int \frac{x}{\sqrt{1-x^2}} dx$$, try the substitution $$x^2=u$$. Can you take it from here?

 

[FlashStorm]

and what v is going to be?

 

[Kurdt]

Its a substitution not an integration by parts.

$$\int f(g(x))\frac{du}{dx}dx=\int f(u)du$$

Actually sid is it not better that x = sin(u) ?

 

[siddharth]

Its a substitution not an integration by parts.

$$\int f(g(x))\frac{du}{dx}dx=\int f(u)du$$

Actually sid is it not better that x = sin(u) ?

Yes, that'd work as well.

 

[FlashStorm]

OMG it worked :P

lot of thanks :)
<3

(didn't substitute x=sin(u) though (I'm not crazy))

 

[FlashStorm]

two new question, and yes I did try to solve it on my own too many times

well that was part of S(sqrt(1-x^2)) which after six hours of trying I didn't manage to solve it.

help? its driving me crazy.
Question 2: solved myself, my brain is probably overheated if I asked weird stuff like it.
and if somebody can guide me how to write here with formal syntax , I'll appreciate it.

 

[siddharth]

well that was part of S(sqrt(1-x^2)) which after six hours of trying I didn't manage to solve it.

help? its driving me crazy.
Question 2: solved myself, my brain is probably overheated if I asked weird stuff like it.
and if somebody can guide me how to write here with formal syntax , I'll appreciate it.

Take a look at the https://www.physicsforums.com/showthread.php?t=8997" thread for this forum. Also, you can click on the latex images to see the code.

To find, $$\int \sqrt{1-x^2} dx$$, try the substitution x=sin(u). Can you take it from here?

 

[FlashStorm]

made it :P

Take a look at the https://www.physicsforums.com/showthread.php?t=8997" thread for this forum. Also, you can click on the latex images to see the code.

To find, $$\int \sqrt{1-x^2} dx$$, try the substitution x=sin(u). Can you take it from here?

Mmm I already solved it yesterday without substituting :)

if you want to know how i did ill be glad to tell.