I’m trying to find a closed form for this integral.Any help is appreciated.Thanks $$I=\int_0^{1}\frac{{ \arcsin}({x^2})}{\sqrt{1-x^2}}dx$$
2026-03-27 18:49:44.1774637384
Closed form for this integral $I=\int_0^{1}\frac{{\arcsin}({x^2})}{\sqrt{1-x^2}}dx$
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As already said in comments, it does not seem that the antiderivative of the integrand exists.
Concerning the integral, a CAS found something you will not like very much $$I=\frac{\pi }{4} \, _4F_3\left(\frac{1}{2},\frac{1}{2},\frac{3}{4},\frac{5}{4};1,\frac{3}{2},\frac{3}{ 2};1\right)$$ where appears the generalized hypergeometric function.
Numerically, $$I\approx 0.9552018064811796875605004$$