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

  • Thread starter Maiko
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  • #1
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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...
 

Answers and Replies

  • #2
256
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Oops, bad advice. Sorry
 
  • #3
Hi, the your integrated is resolved by wolframalpha.com.
Here's the image:

<< Complete solution removed by Hootenanny >>
 
  • #4
216
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Use the substitution tan(x) = t

[tex]sin^2(x)=\frac{tan^2(x)}{1+tan^2(x)}=\frac{t^2}{1+t^2}[/tex]

[tex]cos^2(x)=\frac{1}{1+tan^2(x)}=\frac{1}{1+t^2}[/tex]

[tex]dx=\frac{dt}{1+t^2}[/tex]

Or even better, you can use the substitution cos(x)=t
 
  • #5
726
1
You could also use the substitution u = cosx. Then your integral turns into [tex] - \int \sqrt[]{1+u^2} du [/tex].

Do you recognize this integral now?
 

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