26 views

Skip to first unread message

Jan 31, 2023, 6:07:08 AMJan 31

to

This was an interesting error from FriCAS

-> integrate(x*(-b+a*x^2)^(1/2)*(b-a*x^2+c*x*(-b+a*x^2)^(1/2))^(-3/2),x)

>> Error detected within library code:

Denominator not equal to 1

The answer is

In[415]:= IntegrateAlgebraic[x*(-b + a*x^2)^(1/2)*(b - a*x^2 + c*x*(-b + a*x^2)^(1/2))^(-3/2), x]

Out[415]= (2 Sqrt[-b + a x^2])/((a - c^2) Sqrt[b - a x^2 + c x Sqrt[-b + a x^2]]) -

ArcTan[((Sqrt[a] Sqrt[-b + a x^2])/Sqrt[a - Sqrt[a] c] - (c Sqrt[-b + a x^2])/Sqrt[a - Sqrt[a] c])/Sqrt[b - a x^2 + c x Sqrt[-b + a x^2]]]/((Sqrt[a] - c) Sqrt[a - Sqrt[a] c]) -

ArcTan[((Sqrt[a] Sqrt[-b + a x^2])/Sqrt[a + Sqrt[a] c] + (c Sqrt[-b + a x^2])/Sqrt[a + Sqrt[a] c])/Sqrt[b - a x^2 + c x Sqrt[-b + a x^2]]]/((Sqrt[a] + c) Sqrt[a + Sqrt[a] c])

-> integrate(x*(-b+a*x^2)^(1/2)*(b-a*x^2+c*x*(-b+a*x^2)^(1/2))^(-3/2),x)

>> Error detected within library code:

Denominator not equal to 1

The answer is

In[415]:= IntegrateAlgebraic[x*(-b + a*x^2)^(1/2)*(b - a*x^2 + c*x*(-b + a*x^2)^(1/2))^(-3/2), x]

Out[415]= (2 Sqrt[-b + a x^2])/((a - c^2) Sqrt[b - a x^2 + c x Sqrt[-b + a x^2]]) -

ArcTan[((Sqrt[a] Sqrt[-b + a x^2])/Sqrt[a - Sqrt[a] c] - (c Sqrt[-b + a x^2])/Sqrt[a - Sqrt[a] c])/Sqrt[b - a x^2 + c x Sqrt[-b + a x^2]]]/((Sqrt[a] - c) Sqrt[a - Sqrt[a] c]) -

ArcTan[((Sqrt[a] Sqrt[-b + a x^2])/Sqrt[a + Sqrt[a] c] + (c Sqrt[-b + a x^2])/Sqrt[a + Sqrt[a] c])/Sqrt[b - a x^2 + c x Sqrt[-b + a x^2]]]/((Sqrt[a] + c) Sqrt[a + Sqrt[a] c])

Reply all

Reply to author

Forward

0 new messages

Search

Clear search

Close search

Google apps

Main menu