# Integrate sinx*sqrt(1+((cosx)^2))dx

1. Feb 8, 2009

### Maiko

1. The problem statement, all variables and given/known data
Integrate sinx*sqrt(1+((cosx)^2))dx

2. Relevant equations
integral udv = uv - integral vdu

3. The attempt at a solution
I tried integration by parts which is: integral udv = uv - integral vdu
I tried substituting (cosx)^2= 1-(sonx)^2
neither of them seemed to work...

2. Feb 8, 2009

3. Sep 3, 2009

### Wesley Leite

Hi, the your integrated is resolved by wolframalpha.com.
Here's the image:

<< Complete solution removed by Hootenanny >>

4. Sep 3, 2009

### njama

Use the substitution tan(x) = t

$$sin^2(x)=\frac{tan^2(x)}{1+tan^2(x)}=\frac{t^2}{1+t^2}$$

$$cos^2(x)=\frac{1}{1+tan^2(x)}=\frac{1}{1+t^2}$$

$$dx=\frac{dt}{1+t^2}$$

Or even better, you can use the substitution cos(x)=t

5. Sep 3, 2009

### JG89

You could also use the substitution u = cosx. Then your integral turns into $$- \int \sqrt[]{1+u^2} du$$.

Do you recognize this integral now?