Optimal. Leaf size=139 \[ -\frac{45 b^2 c^3 x \sqrt{\frac{b \left (c x^3\right )^{3/2}}{a}+1} \, _2F_1\left (\frac{2}{9},\frac{1}{2};\frac{11}{9};-\frac{b \left (c x^3\right )^{3/2}}{a}\right )}{448 a \sqrt{a+b \left (c x^3\right )^{3/2}}}-\frac{9 b c^3 x \sqrt{a+b \left (c x^3\right )^{3/2}}}{112 a \left (c x^3\right )^{3/2}}-\frac{\sqrt{a+b \left (c x^3\right )^{3/2}}}{8 x^8} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.216143, antiderivative size = 141, normalized size of antiderivative = 1.01, number of steps used = 6, number of rules used = 6, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.286 \[ -\frac{45 b^2 c^3 x \sqrt{\frac{b \left (c x^3\right )^{3/2}}{a}+1} \, _2F_1\left (\frac{2}{9},\frac{1}{2};\frac{11}{9};-\frac{b \left (c x^3\right )^{3/2}}{a}\right )}{448 a \sqrt{a+b \left (c x^3\right )^{3/2}}}-\frac{9 b c^5 x^7 \sqrt{a+b \left (c x^3\right )^{3/2}}}{112 a \left (c x^3\right )^{7/2}}-\frac{\sqrt{a+b \left (c x^3\right )^{3/2}}}{8 x^8} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[a + b*(c*x^3)^(3/2)]/x^9,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{a + b \left (c x^{3}\right )^{\frac{3}{2}}}}{x^{9}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*(c*x**3)**(3/2))**(1/2)/x**9,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.043311, size = 0, normalized size = 0. \[ \int \frac{\sqrt{a+b \left (c x^3\right )^{3/2}}}{x^9} \, dx \]
Verification is Not applicable to the result.
[In] Integrate[Sqrt[a + b*(c*x^3)^(3/2)]/x^9,x]
[Out]
_______________________________________________________________________________________
Maple [F] time = 0.072, size = 0, normalized size = 0. \[ \int{\frac{1}{{x}^{9}}\sqrt{a+b \left ( c{x}^{3} \right ) ^{{\frac{3}{2}}}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*(c*x^3)^(3/2))^(1/2)/x^9,x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{\left (c x^{3}\right )^{\frac{3}{2}} b + a}}{x^{9}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt((c*x^3)^(3/2)*b + a)/x^9,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt((c*x^3)^(3/2)*b + a)/x^9,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{a + b \left (c x^{3}\right )^{\frac{3}{2}}}}{x^{9}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*(c*x**3)**(3/2))**(1/2)/x**9,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{\left (c x^{3}\right )^{\frac{3}{2}} b + a}}{x^{9}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt((c*x^3)^(3/2)*b + a)/x^9,x, algorithm="giac")
[Out]