Optimal. Leaf size=130 \[ -\frac{\sqrt{\frac{\left (\frac{6}{x}-1\right )^4-182 \left (1-\frac{6}{x}\right )^2+613}{\left (\frac{(6-x)^2}{x^2}+\sqrt{613}\right )^2}} \left (\frac{(6-x)^2}{x^2}+\sqrt{613}\right ) x^2 F\left (2 \tan ^{-1}\left (\frac{6-x}{\sqrt [4]{613} x}\right )|\frac{613+91 \sqrt{613}}{1226}\right )}{12 \sqrt [4]{613} \sqrt{3 x^4+15 x^3-44 x^2-6 x+9}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.428497, antiderivative size = 130, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167 \[ -\frac{\sqrt{\frac{\left (\frac{6}{x}-1\right )^4-182 \left (1-\frac{6}{x}\right )^2+613}{\left (\frac{(6-x)^2}{x^2}+\sqrt{613}\right )^2}} \left (\frac{(6-x)^2}{x^2}+\sqrt{613}\right ) x^2 F\left (2 \tan ^{-1}\left (\frac{6-x}{\sqrt [4]{613} x}\right )|\frac{613+91 \sqrt{613}}{1226}\right )}{12 \sqrt [4]{613} \sqrt{3 x^4+15 x^3-44 x^2-6 x+9}} \]
Antiderivative was successfully verified.
[In] Int[1/Sqrt[9 - 6*x - 44*x^2 + 15*x^3 + 3*x^4],x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - 1296 \int ^{- \frac{1}{6} + \frac{1}{x}} \frac{1}{\sqrt{\frac{15116544 x^{4} - 76422528 x^{2} + 7150032}{\left (- 36 x - 6\right )^{4}}} \left (- 36 x - 6\right )^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(3*x**4+15*x**3-44*x**2-6*x+9)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [C] time = 0.202398, size = 826, normalized size = 6.35 \[ -\frac{2 F\left (\sin ^{-1}\left (\sqrt{\frac{\left (x-\text{Root}\left [3 \text{$\#$1}^4+15 \text{$\#$1}^3-44 \text{$\#$1}^2-6 \text{$\#$1}+9\&,1\right ]\right ) \left (\text{Root}\left [3 \text{$\#$1}^4+15 \text{$\#$1}^3-44 \text{$\#$1}^2-6 \text{$\#$1}+9\&,2\right ]-\text{Root}\left [3 \text{$\#$1}^4+15 \text{$\#$1}^3-44 \text{$\#$1}^2-6 \text{$\#$1}+9\&,4\right ]\right )}{\left (x-\text{Root}\left [3 \text{$\#$1}^4+15 \text{$\#$1}^3-44 \text{$\#$1}^2-6 \text{$\#$1}+9\&,2\right ]\right ) \left (\text{Root}\left [3 \text{$\#$1}^4+15 \text{$\#$1}^3-44 \text{$\#$1}^2-6 \text{$\#$1}+9\&,1\right ]-\text{Root}\left [3 \text{$\#$1}^4+15 \text{$\#$1}^3-44 \text{$\#$1}^2-6 \text{$\#$1}+9\&,4\right ]\right )}}\right )|\frac{\left (\text{Root}\left [3 \text{$\#$1}^4+15 \text{$\#$1}^3-44 \text{$\#$1}^2-6 \text{$\#$1}+9\&,2\right ]-\text{Root}\left [3 \text{$\#$1}^4+15 \text{$\#$1}^3-44 \text{$\#$1}^2-6 \text{$\#$1}+9\&,3\right ]\right ) \left (\text{Root}\left [3 \text{$\#$1}^4+15 \text{$\#$1}^3-44 \text{$\#$1}^2-6 \text{$\#$1}+9\&,1\right ]-\text{Root}\left [3 \text{$\#$1}^4+15 \text{$\#$1}^3-44 \text{$\#$1}^2-6 \text{$\#$1}+9\&,4\right ]\right )}{\left (\text{Root}\left [3 \text{$\#$1}^4+15 \text{$\#$1}^3-44 \text{$\#$1}^2-6 \text{$\#$1}+9\&,1\right ]-\text{Root}\left [3 \text{$\#$1}^4+15 \text{$\#$1}^3-44 \text{$\#$1}^2-6 \text{$\#$1}+9\&,3\right ]\right ) \left (\text{Root}\left [3 \text{$\#$1}^4+15 \text{$\#$1}^3-44 \text{$\#$1}^2-6 \text{$\#$1}+9\&,2\right ]-\text{Root}\left [3 \text{$\#$1}^4+15 \text{$\#$1}^3-44 \text{$\#$1}^2-6 \text{$\#$1}+9\&,4\right ]\right )}\right ) \sqrt{\frac{x-\text{Root}\left [3 \text{$\#$1}^4+15 \text{$\#$1}^3-44 \text{$\#$1}^2-6 \text{$\#$1}+9\&,1\right ]}{x-\text{Root}\left [3 \text{$\#$1}^4+15 \text{$\#$1}^3-44 \text{$\#$1}^2-6 \text{$\#$1}+9\&,2\right ]}} \left (x-\text{Root}\left [3 \text{$\#$1}^4+15 \text{$\#$1}^3-44 \text{$\#$1}^2-6 \text{$\#$1}+9\&,2\right ]\right )^2 \sqrt{\frac{x-\text{Root}\left [3 \text{$\#$1}^4+15 \text{$\#$1}^3-44 \text{$\#$1}^2-6 \text{$\#$1}+9\&,3\right ]}{x-\text{Root}\left [3 \text{$\#$1}^4+15 \text{$\#$1}^3-44 \text{$\#$1}^2-6 \text{$\#$1}+9\&,2\right ]}} \sqrt{\frac{x-\text{Root}\left [3 \text{$\#$1}^4+15 \text{$\#$1}^3-44 \text{$\#$1}^2-6 \text{$\#$1}+9\&,4\right ]}{x-\text{Root}\left [3 \text{$\#$1}^4+15 \text{$\#$1}^3-44 \text{$\#$1}^2-6 \text{$\#$1}+9\&,2\right ]}}}{\sqrt{\left (3 x^4+15 x^3-44 x^2-6 x+9\right ) \left (\text{Root}\left [3 \text{$\#$1}^4+15 \text{$\#$1}^3-44 \text{$\#$1}^2-6 \text{$\#$1}+9\&,1\right ]-\text{Root}\left [3 \text{$\#$1}^4+15 \text{$\#$1}^3-44 \text{$\#$1}^2-6 \text{$\#$1}+9\&,3\right ]\right ) \left (\text{Root}\left [3 \text{$\#$1}^4+15 \text{$\#$1}^3-44 \text{$\#$1}^2-6 \text{$\#$1}+9\&,2\right ]-\text{Root}\left [3 \text{$\#$1}^4+15 \text{$\#$1}^3-44 \text{$\#$1}^2-6 \text{$\#$1}+9\&,4\right ]\right )}} \]
Antiderivative was successfully verified.
[In] Integrate[1/Sqrt[9 - 6*x - 44*x^2 + 15*x^3 + 3*x^4],x]
[Out]
_______________________________________________________________________________________
Maple [C] time = 0.911, size = 1182, normalized size = 9.1 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(3*x^4+15*x^3-44*x^2-6*x+9)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{3 \, x^{4} + 15 \, x^{3} - 44 \, x^{2} - 6 \, x + 9}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(3*x^4 + 15*x^3 - 44*x^2 - 6*x + 9),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{1}{\sqrt{3 \, x^{4} + 15 \, x^{3} - 44 \, x^{2} - 6 \, x + 9}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(3*x^4 + 15*x^3 - 44*x^2 - 6*x + 9),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{3 x^{4} + 15 x^{3} - 44 x^{2} - 6 x + 9}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(3*x**4+15*x**3-44*x**2-6*x+9)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{3 \, x^{4} + 15 \, x^{3} - 44 \, x^{2} - 6 \, x + 9}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(3*x^4 + 15*x^3 - 44*x^2 - 6*x + 9),x, algorithm="giac")
[Out]