Optimal. Leaf size=4 \[ \sin ^{-1}(x+4) \]
[Out]
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Rubi [A] time = 0.0197263, antiderivative size = 4, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.176 \[ \sin ^{-1}(x+4) \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[-3 - x]*Sqrt[5 + x]),x]
[Out]
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Rubi in Sympy [A] time = 1.52303, size = 24, normalized size = 6. \[ \operatorname{atan}{\left (- \frac{- 2 x - 8}{2 \sqrt{- x^{2} - 8 x - 15}} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(-3-x)**(1/2)/(5+x)**(1/2),x)
[Out]
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Mathematica [B] time = 0.0163908, size = 42, normalized size = 10.5 \[ \frac{2 \sqrt{x+3} \sqrt{x+5} \sinh ^{-1}\left (\frac{\sqrt{x+3}}{\sqrt{2}}\right )}{\sqrt{-(x+3) (x+5)}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[-3 - x]*Sqrt[5 + x]),x]
[Out]
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Maple [B] time = 0.008, size = 29, normalized size = 7.3 \[{\arcsin \left ( 4+x \right ) \sqrt{ \left ( -3-x \right ) \left ( 5+x \right ) }{\frac{1}{\sqrt{-3-x}}}{\frac{1}{\sqrt{5+x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(-3-x)^(1/2)/(5+x)^(1/2),x)
[Out]
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Maxima [A] time = 0.754736, size = 11, normalized size = 2.75 \[ -\arcsin \left (-x - 4\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x + 5)*sqrt(-x - 3)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.27047, size = 23, normalized size = 5.75 \[ \arctan \left (\frac{x + 4}{\sqrt{x + 5} \sqrt{-x - 3}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x + 5)*sqrt(-x - 3)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.75162, size = 41, normalized size = 10.25 \[ \begin{cases} - 2 i \operatorname{acosh}{\left (\frac{\sqrt{2} \sqrt{x + 5}}{2} \right )} & \text{for}\: \frac{\left |{x + 5}\right |}{2} > 1 \\2 \operatorname{asin}{\left (\frac{\sqrt{2} \sqrt{x + 5}}{2} \right )} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(-3-x)**(1/2)/(5+x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.268886, size = 18, normalized size = 4.5 \[ 2 \, \arcsin \left (\frac{1}{2} \, \sqrt{2} \sqrt{x + 5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x + 5)*sqrt(-x - 3)),x, algorithm="giac")
[Out]