Optimal. Leaf size=40 \[ \frac{\left (a+b x^{3/2}\right )^{4/3}}{2 b^2}-\frac{2 a \sqrt [3]{a+b x^{3/2}}}{b^2} \]
[Out]
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Rubi [A] time = 0.0624712, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ \frac{\left (a+b x^{3/2}\right )^{4/3}}{2 b^2}-\frac{2 a \sqrt [3]{a+b x^{3/2}}}{b^2} \]
Antiderivative was successfully verified.
[In] Int[x^2/(a + b*x^(3/2))^(2/3),x]
[Out]
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Rubi in Sympy [A] time = 7.14871, size = 34, normalized size = 0.85 \[ - \frac{2 a \sqrt [3]{a + b x^{\frac{3}{2}}}}{b^{2}} + \frac{\left (a + b x^{\frac{3}{2}}\right )^{\frac{4}{3}}}{2 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2/(a+b*x**(3/2))**(2/3),x)
[Out]
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Mathematica [A] time = 0.0222897, size = 31, normalized size = 0.78 \[ \frac{\left (b x^{3/2}-3 a\right ) \sqrt [3]{a+b x^{3/2}}}{2 b^2} \]
Antiderivative was successfully verified.
[In] Integrate[x^2/(a + b*x^(3/2))^(2/3),x]
[Out]
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Maple [A] time = 0.004, size = 30, normalized size = 0.8 \[ 2\,{\frac{1/4\, \left ( a+b{x}^{3/2} \right ) ^{4/3}-a\sqrt [3]{a+b{x}^{3/2}}}{{b}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2/(a+b*x^(3/2))^(2/3),x)
[Out]
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Maxima [A] time = 1.44101, size = 41, normalized size = 1.02 \[ \frac{{\left (b x^{\frac{3}{2}} + a\right )}^{\frac{4}{3}}}{2 \, b^{2}} - \frac{2 \,{\left (b x^{\frac{3}{2}} + a\right )}^{\frac{1}{3}} a}{b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(b*x^(3/2) + a)^(2/3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.43604, size = 31, normalized size = 0.78 \[ \frac{{\left (b x^{\frac{3}{2}} + a\right )}^{\frac{1}{3}}{\left (b x^{\frac{3}{2}} - 3 \, a\right )}}{2 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(b*x^(3/2) + a)^(2/3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 5.14262, size = 49, normalized size = 1.22 \[ \begin{cases} - \frac{3 a \sqrt [3]{a + b x^{\frac{3}{2}}}}{2 b^{2}} + \frac{x^{\frac{3}{2}} \sqrt [3]{a + b x^{\frac{3}{2}}}}{2 b} & \text{for}\: b \neq 0 \\\frac{x^{3}}{3 a^{\frac{2}{3}}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2/(a+b*x**(3/2))**(2/3),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{2}}{{\left (b x^{\frac{3}{2}} + a\right )}^{\frac{2}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(b*x^(3/2) + a)^(2/3),x, algorithm="giac")
[Out]