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Full Version: [Discussion] Solving the Limit Problem
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Nonsense, paste code
Code:
`limit((∫(∫(sin(t)*atan(1+t),t,0,u^2),u,0,x))/(x^3*((x+1)^(1/3)-1)^2),x,0)`
xcas get
Code:
`"Limit: Max order reached or unable to make series expansion Error: Bad Argument Value"`

mathematica also calculated for a long time
Code:
```Limit[Integrate[Sin[t]*ArcTan[1 + t], {u, 0, x}, {t, 0, u^2}]/(  x^3*((x + 1)^(1/3) - 1)^2), x -> 0]```

Surprisingly, the Ti Nspire CX CII CAS is calculated

In fact, the hp prime can be calculated, and it needs to be replaced by another method.

let f(t)=sin(t)*atan(1+t)

Code:
`series((∫(∫(f(t),t,0,u^2),u,0,x)/(x^3*((x+1)^(1/3)-1)^2)),equal(x,0),1)`

hp prime get
Code:
`(3*f(0)/x^2)+(2*f(0)/x)+(9/10)*(function_diff(f))(0)-(1/9)*f(0)+((3/5)*(function_diff(f))(0)+(2/27)*f(0))*x+x^2*order_size(x)`

We find f (0) = 0 and substitute it into the result,Get the limit
Code:
`((9/10)*∂(sin(t)*atan(1+t),t)|(equal(t,0)))`
hp prime get
Code:
`9*π/40`
Several perverted integrals
(i)
Code:
`evalf(int(1/(1+e^(1/x)),x,-1,1))`
xcas get
Code:
`"Unidirectional limits are distincts 1,0 Error: Bad Argument Valu"`

(ii)
Code:
`int(x^2*tan(x)^2+x^2+2*x*tan(x)+1,x)`
`x+x*tan(x)`
`simplify(int((x*tan(x)+ln(x*cos(x))-1)/ln(x*cos(x))^2,x))`
`x/ln(x*ln(x))`