Optimal. Leaf size=57 \[ \frac{1}{4} a^2 x^3 \sqrt{c x^2}+\frac{2}{5} a b x^4 \sqrt{c x^2}+\frac{1}{6} b^2 x^5 \sqrt{c x^2} \]
[Out]
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Rubi [A] time = 0.0398942, antiderivative size = 57, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ \frac{1}{4} a^2 x^3 \sqrt{c x^2}+\frac{2}{5} a b x^4 \sqrt{c x^2}+\frac{1}{6} b^2 x^5 \sqrt{c x^2} \]
Antiderivative was successfully verified.
[In] Int[x^2*Sqrt[c*x^2]*(a + b*x)^2,x]
[Out]
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Rubi in Sympy [A] time = 12.6069, size = 51, normalized size = 0.89 \[ \frac{a^{2} x^{3} \sqrt{c x^{2}}}{4} + \frac{2 a b x^{4} \sqrt{c x^{2}}}{5} + \frac{b^{2} x^{5} \sqrt{c x^{2}}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2*(b*x+a)**2*(c*x**2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.00858386, size = 35, normalized size = 0.61 \[ \frac{1}{60} x^3 \sqrt{c x^2} \left (15 a^2+24 a b x+10 b^2 x^2\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^2*Sqrt[c*x^2]*(a + b*x)^2,x]
[Out]
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Maple [A] time = 0.006, size = 32, normalized size = 0.6 \[{\frac{{x}^{3} \left ( 10\,{b}^{2}{x}^{2}+24\,abx+15\,{a}^{2} \right ) }{60}\sqrt{c{x}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2*(b*x+a)^2*(c*x^2)^(1/2),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(sqrt(c*x^2)*(b*x + a)^2*x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.194943, size = 45, normalized size = 0.79 \[ \frac{1}{60} \,{\left (10 \, b^{2} x^{5} + 24 \, a b x^{4} + 15 \, a^{2} x^{3}\right )} \sqrt{c x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(c*x^2)*(b*x + a)^2*x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.38453, size = 61, normalized size = 1.07 \[ \frac{a^{2} \sqrt{c} x^{3} \sqrt{x^{2}}}{4} + \frac{2 a b \sqrt{c} x^{4} \sqrt{x^{2}}}{5} + \frac{b^{2} \sqrt{c} x^{5} \sqrt{x^{2}}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2*(b*x+a)**2*(c*x**2)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.20649, size = 47, normalized size = 0.82 \[ \frac{1}{60} \,{\left (10 \, b^{2} x^{6}{\rm sign}\left (x\right ) + 24 \, a b x^{5}{\rm sign}\left (x\right ) + 15 \, a^{2} x^{4}{\rm sign}\left (x\right )\right )} \sqrt{c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(c*x^2)*(b*x + a)^2*x^2,x, algorithm="giac")
[Out]