Optimal. Leaf size=116 \[ -\frac{4 a^3 \left (a+b \left (c x^3\right )^{3/2}\right )^{3/2}}{27 b^4 c^6}+\frac{4 a^2 \left (a+b \left (c x^3\right )^{3/2}\right )^{5/2}}{15 b^4 c^6}+\frac{4 \left (a+b \left (c x^3\right )^{3/2}\right )^{9/2}}{81 b^4 c^6}-\frac{4 a \left (a+b \left (c x^3\right )^{3/2}\right )^{7/2}}{21 b^4 c^6} \]
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Rubi [A] time = 0.16921, antiderivative size = 116, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ -\frac{4 a^3 \left (a+b \left (c x^3\right )^{3/2}\right )^{3/2}}{27 b^4 c^6}+\frac{4 a^2 \left (a+b \left (c x^3\right )^{3/2}\right )^{5/2}}{15 b^4 c^6}+\frac{4 \left (a+b \left (c x^3\right )^{3/2}\right )^{9/2}}{81 b^4 c^6}-\frac{4 a \left (a+b \left (c x^3\right )^{3/2}\right )^{7/2}}{21 b^4 c^6} \]
Antiderivative was successfully verified.
[In] Int[x^17*Sqrt[a + b*(c*x^3)^(3/2)],x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int x^{17} \sqrt{a + b \left (c x^{3}\right )^{\frac{3}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**17*(a+b*(c*x**3)**(3/2))**(1/2),x)
[Out]
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Mathematica [A] time = 0.105557, size = 0, normalized size = 0. \[ \int x^{17} \sqrt{a+b \left (c x^3\right )^{3/2}} \, dx \]
Verification is Not applicable to the result.
[In] Integrate[x^17*Sqrt[a + b*(c*x^3)^(3/2)],x]
[Out]
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Maple [F] time = 0.073, size = 0, normalized size = 0. \[ \int{x}^{17}\sqrt{a+b \left ( c{x}^{3} \right ) ^{{\frac{3}{2}}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^17*(a+b*(c*x^3)^(3/2))^(1/2),x)
[Out]
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Maxima [A] time = 1.34232, size = 115, normalized size = 0.99 \[ \frac{4 \,{\left (\frac{35 \,{\left (\left (c x^{3}\right )^{\frac{3}{2}} b + a\right )}^{\frac{9}{2}}}{b^{4}} - \frac{135 \,{\left (\left (c x^{3}\right )^{\frac{3}{2}} b + a\right )}^{\frac{7}{2}} a}{b^{4}} + \frac{189 \,{\left (\left (c x^{3}\right )^{\frac{3}{2}} b + a\right )}^{\frac{5}{2}} a^{2}}{b^{4}} - \frac{105 \,{\left (\left (c x^{3}\right )^{\frac{3}{2}} b + a\right )}^{\frac{3}{2}} a^{3}}{b^{4}}\right )}}{2835 \, c^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt((c*x^3)^(3/2)*b + a)*x^17,x, algorithm="maxima")
[Out]
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Fricas [A] time = 2.30362, size = 117, normalized size = 1.01 \[ \frac{4 \,{\left (35 \, b^{4} c^{6} x^{18} - 6 \, a^{2} b^{2} c^{3} x^{9} - 16 \, a^{4} +{\left (5 \, a b^{3} c^{4} x^{12} + 8 \, a^{3} b c x^{3}\right )} \sqrt{c x^{3}}\right )} \sqrt{\sqrt{c x^{3}} b c x^{3} + a}}{2835 \, b^{4} c^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt((c*x^3)^(3/2)*b + a)*x^17,x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**17*(a+b*(c*x**3)**(3/2))**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.222591, size = 193, normalized size = 1.66 \[ \frac{4 \,{\left (\frac{16 \, \sqrt{a c^{3}} a^{4}}{b^{4} c^{5}} - \frac{105 \,{\left (\sqrt{c x} b c^{4} x^{4} + a c^{3}\right )}^{\frac{3}{2}} a^{3} c^{9} - 189 \,{\left (\sqrt{c x} b c^{4} x^{4} + a c^{3}\right )}^{\frac{5}{2}} a^{2} c^{6} + 135 \,{\left (\sqrt{c x} b c^{4} x^{4} + a c^{3}\right )}^{\frac{7}{2}} a c^{3} - 35 \,{\left (\sqrt{c x} b c^{4} x^{4} + a c^{3}\right )}^{\frac{9}{2}}}{b^{4} c^{17}}\right )}{\left | c \right |}}{2835 \, c^{\frac{7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt((c*x^3)^(3/2)*b + a)*x^17,x, algorithm="giac")
[Out]