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

[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...

[rochfor1]

Oops, bad advice. Sorry

[Wesley Leite]

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

<< Complete solution removed by Hootenanny >>

[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

[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?