# Calc II Integration with trig

1. Sep 7, 2010

### Agent M27

1. The problem statement, all variables and given/known data
$$\int\frac{dx}{\sqrt{x}\sqrt{1-x}}$$

2. Relevant equations

$$\int\frac{du}{\sqrt{a^{2}-u^{2}}}= arcsin\frac{u}{a} + C$$

3. The attempt at a solution

u$$^{2}$$=x

dx=2u du

$$\int\frac{2u}{u\sqrt{1-u^{2}}}du$$

2$$\int\frac{du}{\sqrt{1-u^{2}}} = 2arcsin\frac{u}{a} + C$$

=2arcsin($$\sqrt{x}$$) + C

But the book gives the answer to be 2arcsec($$\sqrt{x}$$) + C, which I do not understand how they achieved that answer. Any help would be appreciated. Thank you.

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

2. Relevant equations

3. The attempt at a solution

2. Sep 7, 2010

### NastyAccident

Well, rest easy.

I just checked your work and it is definitely $$2arcsin(sqrt(x)) + C$$. The answer that was given by the book is an unfortunate typo.

Also, u = sqrt(x) is another way to use substitution.

3. Sep 8, 2010

### Agent M27

That is good to hear, I felt like I was going crazy. BTW I originally set u=sqrt(x), but when finding du, it was simpler to square both sides. I don't like radicals... Thank you.

Joe