Optimal. Leaf size=60 \[ \frac{1}{4} a^2 c x^3 \sqrt{c x^2}+\frac{2}{5} a b c x^4 \sqrt{c x^2}+\frac{1}{6} b^2 c x^5 \sqrt{c x^2} \]
[Out]
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Rubi [A] time = 0.0381567, antiderivative size = 60, 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 \[ \frac{1}{4} a^2 c x^3 \sqrt{c x^2}+\frac{2}{5} a b c x^4 \sqrt{c x^2}+\frac{1}{6} b^2 c x^5 \sqrt{c x^2} \]
Antiderivative was successfully verified.
[In] Int[(c*x^2)^(3/2)*(a + b*x)^2,x]
[Out]
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Rubi in Sympy [A] time = 11.0313, size = 56, normalized size = 0.93 \[ \frac{a^{2} c x^{3} \sqrt{c x^{2}}}{4} + \frac{2 a b c x^{4} \sqrt{c x^{2}}}{5} + \frac{b^{2} c x^{5} \sqrt{c x^{2}}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**2)**(3/2)*(b*x+a)**2,x)
[Out]
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Mathematica [A] time = 0.011928, size = 33, normalized size = 0.55 \[ \frac{1}{60} x \left (c x^2\right )^{3/2} \left (15 a^2+24 a b x+10 b^2 x^2\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(c*x^2)^(3/2)*(a + b*x)^2,x]
[Out]
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Maple [A] time = 0.006, size = 30, normalized size = 0.5 \[{\frac{x \left ( 10\,{b}^{2}{x}^{2}+24\,abx+15\,{a}^{2} \right ) }{60} \left ( c{x}^{2} \right ) ^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^2)^(3/2)*(b*x+a)^2,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((c*x^2)^(3/2)*(b*x + a)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.204318, size = 49, normalized size = 0.82 \[ \frac{1}{60} \,{\left (10 \, b^{2} c x^{5} + 24 \, a b c x^{4} + 15 \, a^{2} c x^{3}\right )} \sqrt{c x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2)^(3/2)*(b*x + a)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.36483, size = 60, normalized size = 1. \[ \frac{a^{2} c^{\frac{3}{2}} x \left (x^{2}\right )^{\frac{3}{2}}}{4} + \frac{2 a b c^{\frac{3}{2}} x^{2} \left (x^{2}\right )^{\frac{3}{2}}}{5} + \frac{b^{2} c^{\frac{3}{2}} x^{3} \left (x^{2}\right )^{\frac{3}{2}}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**2)**(3/2)*(b*x+a)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.207233, size = 47, normalized size = 0.78 \[ \frac{1}{60} \,{\left (10 \, b^{2} x^{6}{\rm sign}\left (x\right ) + 24 \, a b x^{5}{\rm sign}\left (x\right ) + 15 \, a^{2} x^{4}{\rm sign}\left (x\right )\right )} c^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2)^(3/2)*(b*x + a)^2,x, algorithm="giac")
[Out]