=∫(cosx+cosx/sin2x)sinx+cosxdx....is that any help?
I would like to pause here and consider the domain of x.
To take square root, must have cosx≥0, so −π/2≤x≤π/2.
Numerator sinx+cosx≥0⟹−π/4≤x≤3π/4.
Finally, can't have cosx=0 in the denominator, so x=π/2.
The complete domain is −π/4≤x<π/2.
Since the domain includes points in both 4th and 1st quadrants, the cosine may not the best choice for substitution because it is not 1:1 with x...
I was very impressed by the algebraic tricks you used on the max(x^4y + xy^4) question, using the constraint (x+y)=1 to simplify the functional form. Can you do something like that here?? I will keep looking..
This site uses cookies to help personalise content, tailor your experience and to keep you logged in if you register.
By continuing to use this site, you are consenting to our use of cookies.