Optimal. Leaf size=101 \[ \frac{b^2 c^3 \tanh ^{-1}\left (\frac{\sqrt{a+b \left (c x^3\right )^{3/2}}}{\sqrt{a}}\right )}{18 a^{3/2}}-\frac{b c^3 \sqrt{a+b \left (c x^3\right )^{3/2}}}{18 a \left (c x^3\right )^{3/2}}-\frac{\sqrt{a+b \left (c x^3\right )^{3/2}}}{9 x^9} \]
[Out]
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Rubi [A] time = 0.142428, antiderivative size = 104, normalized size of antiderivative = 1.03, number of steps used = 6, number of rules used = 6, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.286 \[ \frac{b^2 c^3 \tanh ^{-1}\left (\frac{\sqrt{a+b \left (c x^3\right )^{3/2}}}{\sqrt{a}}\right )}{18 a^{3/2}}-\frac{b c^6 x^9 \sqrt{a+b \left (c x^3\right )^{3/2}}}{18 a \left (c x^3\right )^{9/2}}-\frac{\sqrt{a+b \left (c x^3\right )^{3/2}}}{9 x^9} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[a + b*(c*x^3)^(3/2)]/x^10,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{a + b \left (c x^{3}\right )^{\frac{3}{2}}}}{x^{10}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*(c*x**3)**(3/2))**(1/2)/x**10,x)
[Out]
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Mathematica [A] time = 0.0436025, size = 0, normalized size = 0. \[ \int \frac{\sqrt{a+b \left (c x^3\right )^{3/2}}}{x^{10}} \, dx \]
Verification is Not applicable to the result.
[In] Integrate[Sqrt[a + b*(c*x^3)^(3/2)]/x^10,x]
[Out]
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Maple [F] time = 0.067, size = 0, normalized size = 0. \[ \int{\frac{1}{{x}^{10}}\sqrt{a+b \left ( c{x}^{3} \right ) ^{{\frac{3}{2}}}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*(c*x^3)^(3/2))^(1/2)/x^10,x)
[Out]
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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((c*x^3)^(3/2)*b + a)/x^10,x, algorithm="maxima")
[Out]
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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^10,x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{a + b \left (c x^{3}\right )^{\frac{3}{2}}}}{x^{10}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*(c*x**3)**(3/2))**(1/2)/x**10,x)
[Out]
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GIAC/XCAS [A] time = 0.740945, size = 158, normalized size = 1.56 \[ -\frac{1}{18} \, b^{2} c^{\frac{13}{2}}{\left (\frac{\arctan \left (\frac{\sqrt{\sqrt{c x} b c^{4} x^{4} + a c^{3}}}{\sqrt{-a c} c}\right )}{\sqrt{-a c} a c^{4}} + \frac{\sqrt{\sqrt{c x} b c^{4} x^{4} + a c^{3}} a c^{3} +{\left (\sqrt{c x} b c^{4} x^{4} + a c^{3}\right )}^{\frac{3}{2}}}{a b^{2} c^{12} x^{9}}\right )}{\left | c \right |} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt((c*x^3)^(3/2)*b + a)/x^10,x, algorithm="giac")
[Out]