Some integrates problems on Rubi (Avoid opening too many issues)

[asukaminato0721]

Rubi can't deal with tan(x) but can deal with sin(x)/cos(x)

this can't work.

Int[x /(1 + x Tan[x]), x] // Steps

but this can.

Int[(x Cos[x])/(Cos[x] + x Sin[x]), x] // Steps

[asukaminato0721]

I feel not good to post to many issues. So I choose to continue in this issue.

This , mathematica gives a primary solution. But Rubi gives a complex solution.

Log[Cos[x] + Sqrt[Cos[2 x]]]/Sin[x]^2

https://artofproblemsolving.com/community/c7h1344572p7316265

[mariuszi28cg]

Rubi Can't find:

Int[x/Sqrt[Exp[x] + (x + 2)^2], x]

but solution is:

x - 2 Log[(x + 2) + Sqrt[Exp[x] + (x + 2)^2]]+C

[asukaminato0721]

(x - 2)/Sqrt[E^x - x^2]

the answer is below.

https://www.zhihu.com/question/397590932/answer/1248294422

\int \frac{x-2}{\sqrt{e^x-x^2}}dx=\begin{cases} \arcsin(1-2x^2e^{-x})+C,&x>0\\ -\arcsin(1-2x^2e^{-x})+C+\pi,&x<0 \end{cases}