Is the supposed to be there? Otherwise you have
Hey, I was wondering if anyone could help me with the following integration:
integrate 1/(1+tcosx) wrt x from 0 to pi. I know you have to make the substitution u=tan(x/2), but I've been trying for ages and can't seem to get the answer. =(
Thanks in advance!!
Hello,
Let
By substituting , we have :
(because )
So (u was just a dummy variable).
Then
So finally,
I have to think how to continue...
I think I finally found it (after multiple careless mistakes )
You can note that this latter integrand is symmetric with respect to
Hence
We know that . So :
Now use Weierstrass substitution : , where . -->
But then, we know that an antiderivative of is
Therefore :
Note that everything is okay because