# Integration by parts

1. Feb 11, 2009

### crm08

1. The problem statement, all variables and given/known data

$$\int(sin(x)^{-1}), dx$$

2. Relevant equations

*By Parts Formula: f(x)g(x) - $$\int(g(x) f'(x)) dx$$

Also for d/dx sin(x)^{-1} I used 1/sqrt(1-x^{2})

3. The attempt at a solution

Just started learning this method, I tried letting f(x) = sin(x)^{-1} and g(x) = dx but nothing really simplified, can someone help with selecting the correct g(x) and f(x), Thanks

Last edited: Feb 11, 2009
2. Feb 11, 2009

### cristo

Staff Emeritus
Is the function you're trying to integrate here the inverse function of sin(x)? If so, it should be denoted $$\arcsin(x)=\sin^{-1}(x)$$

This isn't a formula, since you haven't specified what it is equal to! The formula I would use is $$\int v du=uv-\int udv$$. Is this the formula you have been taught? If not, what is the formula you have been taught?

3. Feb 11, 2009

### crm08

Yes, the problem is asking for the integral of arcsin(x), and also yes, that is the formula we are using, my "u's" and "v's" look a lot alike sometimes so I replaced them with f(x) and g(x), sorry about the confusion

4. Feb 11, 2009

### cristo

Staff Emeritus
Ok, so your selection was $u=\sin^{-1}(x) \,\, , \,\, dv=dx$, right? So, what went wrong? This is the choice that I would make!

5. Feb 11, 2009

### crm08

Ok nevermind I got it now, I was working towards an answer to this problem that my 89 gave me but I typed it in wrong, I see how to to it now, the answer being:

x*arcsin(x) + sqrt(1-x^2)