Optimal. Leaf size=44 \[ \frac{3 x \left (3 a+b x^2\right )}{2 \left (a-b x^2\right )^{4/3}}+\frac{9 x}{2 \sqrt [3]{a-b x^2}} \]
[Out]
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Rubi [A] time = 0.0511061, antiderivative size = 44, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083 \[ \frac{3 x \left (3 a+b x^2\right )}{2 \left (a-b x^2\right )^{4/3}}+\frac{9 x}{2 \sqrt [3]{a-b x^2}} \]
Antiderivative was successfully verified.
[In] Int[(3*a + b*x^2)^2/(a - b*x^2)^(7/3),x]
[Out]
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Rubi in Sympy [A] time = 21.476, size = 37, normalized size = 0.84 \[ \frac{9 x}{2 \sqrt [3]{a - b x^{2}}} + \frac{3 x \left (3 a + b x^{2}\right )}{2 \left (a - b x^{2}\right )^{\frac{4}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+3*a)**2/(-b*x**2+a)**(7/3),x)
[Out]
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Mathematica [A] time = 0.0381237, size = 24, normalized size = 0.55 \[ \frac{9 a x-3 b x^3}{\left (a-b x^2\right )^{4/3}} \]
Antiderivative was successfully verified.
[In] Integrate[(3*a + b*x^2)^2/(a - b*x^2)^(7/3),x]
[Out]
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Maple [A] time = 0.008, size = 24, normalized size = 0.6 \[ 3\,{\frac{x \left ( -b{x}^{2}+3\,a \right ) }{ \left ( -b{x}^{2}+a \right ) ^{4/3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+3*a)^2/(-b*x^2+a)^(7/3),x)
[Out]
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Maxima [A] time = 1.48278, size = 45, normalized size = 1.02 \[ \frac{3 \,{\left (b x^{3} - 3 \, a x\right )}}{{\left (b x^{2} - a\right )}{\left (-b x^{2} + a\right )}^{\frac{1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + 3*a)^2/(-b*x^2 + a)^(7/3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.261818, size = 57, normalized size = 1.3 \[ -\frac{3 \,{\left (b x^{3} - 3 \, a x\right )}{\left (-b x^{2} + a\right )}^{\frac{2}{3}}}{b^{2} x^{4} - 2 \, a b x^{2} + a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + 3*a)^2/(-b*x^2 + a)^(7/3),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (3 a + b x^{2}\right )^{2}}{\left (a - b x^{2}\right )^{\frac{7}{3}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+3*a)**2/(-b*x**2+a)**(7/3),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (b x^{2} + 3 \, a\right )}^{2}}{{\left (-b x^{2} + a\right )}^{\frac{7}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + 3*a)^2/(-b*x^2 + a)^(7/3),x, algorithm="giac")
[Out]