# Correct way of simplifying the result of an integral

Many times Mathematica gives enormous results to simple problems. One uses the program more for trouble than for not knowing how to solve the problem. As an ejemplo I present this integral that Mathematica turns out quickly but with a huge result, even though the attempt to simplify did not reach the result made by hand.

• The question arises: what for? is not it art for art's sake? Commented Sep 1, 2019 at 9:39
• E.g. Integrate[1/Sqrt[1 + Sin[x]], {x, -Pi/4, Pi/3}] // FullSimplify performs $$\frac{\log \left(\sqrt{2}+2\right)+\log \left(5-2 \sqrt{6}\right)-2 \log \left(2-\sqrt{\sqrt{2}+2}\right)}{\sqrt{2}}.$$ Is not it enough simple? Commented Dec 26, 2019 at 9:49

Many times Mathematica gives enormous results to simple problems

If Simplify still does not help reduce the antiderivative to what you like, you could always try Rubi

<< Rubi
integrand = 1/Sqrt[1 + Sin[x]];
sol = Int[integrand, x]


 D[sol, x] // Simplify
`

There is a page here which compares different integrators with the size of antiderivatives they give.

• wow , I didn't know that extension, great thanks Commented Sep 4, 2019 at 0:43