Optimal. Leaf size=95 \[ -\frac{b^3 \tanh ^{-1}\left (\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right )}{24 a^{5/2}}+\frac{b^2 \sqrt{a+b x^3}}{24 a^2 x^3}-\frac{\sqrt{a+b x^3}}{9 x^9}-\frac{b \sqrt{a+b x^3}}{36 a x^6} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.137731, antiderivative size = 95, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 5, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333 \[ -\frac{b^3 \tanh ^{-1}\left (\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right )}{24 a^{5/2}}+\frac{b^2 \sqrt{a+b x^3}}{24 a^2 x^3}-\frac{\sqrt{a+b x^3}}{9 x^9}-\frac{b \sqrt{a+b x^3}}{36 a x^6} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[a + b*x^3]/x^10,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 13.5744, size = 82, normalized size = 0.86 \[ - \frac{\sqrt{a + b x^{3}}}{9 x^{9}} - \frac{b \sqrt{a + b x^{3}}}{36 a x^{6}} + \frac{b^{2} \sqrt{a + b x^{3}}}{24 a^{2} x^{3}} - \frac{b^{3} \operatorname{atanh}{\left (\frac{\sqrt{a + b x^{3}}}{\sqrt{a}} \right )}}{24 a^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**(1/2)/x**10,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.276076, size = 79, normalized size = 0.83 \[ \frac{\sqrt{a+b x^3} \left (\frac{a \left (-8 a^2-2 a b x^3+3 b^2 x^6\right )}{x^9}-\frac{3 b^3 \tanh ^{-1}\left (\sqrt{\frac{b x^3}{a}+1}\right )}{\sqrt{\frac{b x^3}{a}+1}}\right )}{72 a^3} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[a + b*x^3]/x^10,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.031, size = 76, normalized size = 0.8 \[ -{\frac{{b}^{3}}{24}{\it Artanh} \left ({1\sqrt{b{x}^{3}+a}{\frac{1}{\sqrt{a}}}} \right ){a}^{-{\frac{5}{2}}}}-{\frac{1}{9\,{x}^{9}}\sqrt{b{x}^{3}+a}}-{\frac{b}{36\,{x}^{6}a}\sqrt{b{x}^{3}+a}}+{\frac{{b}^{2}}{24\,{x}^{3}{a}^{2}}\sqrt{b{x}^{3}+a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^(1/2)/x^10,x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x^3 + a)/x^10,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.22812, size = 1, normalized size = 0.01 \[ \left [\frac{3 \, b^{3} x^{9} \log \left (\frac{{\left (b x^{3} + 2 \, a\right )} \sqrt{a} - 2 \, \sqrt{b x^{3} + a} a}{x^{3}}\right ) + 2 \,{\left (3 \, b^{2} x^{6} - 2 \, a b x^{3} - 8 \, a^{2}\right )} \sqrt{b x^{3} + a} \sqrt{a}}{144 \, a^{\frac{5}{2}} x^{9}}, \frac{3 \, b^{3} x^{9} \arctan \left (\frac{a}{\sqrt{b x^{3} + a} \sqrt{-a}}\right ) +{\left (3 \, b^{2} x^{6} - 2 \, a b x^{3} - 8 \, a^{2}\right )} \sqrt{b x^{3} + a} \sqrt{-a}}{72 \, \sqrt{-a} a^{2} x^{9}}\right ] \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x^3 + a)/x^10,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 21.4166, size = 129, normalized size = 1.36 \[ - \frac{a}{9 \sqrt{b} x^{\frac{21}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{5 \sqrt{b}}{36 x^{\frac{15}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} + \frac{b^{\frac{3}{2}}}{72 a x^{\frac{9}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} + \frac{b^{\frac{5}{2}}}{24 a^{2} x^{\frac{3}{2}} \sqrt{\frac{a}{b x^{3}} + 1}} - \frac{b^{3} \operatorname{asinh}{\left (\frac{\sqrt{a}}{\sqrt{b} x^{\frac{3}{2}}} \right )}}{24 a^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**(1/2)/x**10,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.232973, size = 108, normalized size = 1.14 \[ \frac{1}{72} \, b^{3}{\left (\frac{3 \, \arctan \left (\frac{\sqrt{b x^{3} + a}}{\sqrt{-a}}\right )}{\sqrt{-a} a^{2}} + \frac{3 \,{\left (b x^{3} + a\right )}^{\frac{5}{2}} - 8 \,{\left (b x^{3} + a\right )}^{\frac{3}{2}} a - 3 \, \sqrt{b x^{3} + a} a^{2}}{a^{2} b^{3} x^{9}}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x^3 + a)/x^10,x, algorithm="giac")
[Out]