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

[Maiko]

Homework Statement

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

Homework Equations

integral udv = uv - integral vdu

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?