- #1
Substitution won't help much here. This is not integrable in the elementary functions. Ignoring the first part, which is easy, the result is a constant times the difference between an elliptical integral of the first kind and an elliptical integral of the second kind.Do you know substitution?
sin(x)=u is a possible approach, and that method might work as well.
Hint: Rewrite the numerator ##-\sin^2(x)## as ##c-(\sin^2(x)+c)##.
Substitution won't help much here. This is not integrable in the elementary functions. Ignoring the first part, which is easy, the result is a constant times the difference between an elliptical integral of the first kind and an elliptical integral of the second kind.
The *denominator* is a square root. The *numerator* is -sin(x)^{2}.Hi,
The numerator is a square root. I can't see how rewriting the numerator in such a way
will lead me to the expected result.
Please can you give further indications?
The *denominator* is a square root. The *numerator* is -sin(x)^{2}.
Did you read my first post? You can try all the substitutions you want and you will *never* be able to find an analytic solution to this problem in the elementary functions. This problem is not integrable in the elementary functions. Fortunately, there are two special functions that are very applicable to this problem, the elliptical integrals of the first and second kind. The standard definitions of these functions areSorry
Yeah I see. I have tried but that won't help either.
DId you get any result with that substitution?
The problem is the last term of the integration by part
that always contains at the denominator √([sin]^{2}(x)+c)