Optimal. Leaf size=57 \[ \frac{1}{5} a^2 x^4 \sqrt{c x^2}+\frac{1}{3} a b x^5 \sqrt{c x^2}+\frac{1}{7} b^2 x^6 \sqrt{c x^2} \]
[Out]
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Rubi [A] time = 0.0418007, 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 \[ \frac{1}{5} a^2 x^4 \sqrt{c x^2}+\frac{1}{3} a b x^5 \sqrt{c x^2}+\frac{1}{7} b^2 x^6 \sqrt{c x^2} \]
Antiderivative was successfully verified.
[In] Int[x^3*Sqrt[c*x^2]*(a + b*x)^2,x]
[Out]
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Rubi in Sympy [A] time = 17.7589, size = 49, normalized size = 0.86 \[ \frac{a^{2} x^{4} \sqrt{c x^{2}}}{5} + \frac{a b x^{5} \sqrt{c x^{2}}}{3} + \frac{b^{2} x^{6} \sqrt{c x^{2}}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3*(b*x+a)**2*(c*x**2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.00886833, size = 35, normalized size = 0.61 \[ \frac{1}{105} x^4 \sqrt{c x^2} \left (21 a^2+35 a b x+15 b^2 x^2\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^3*Sqrt[c*x^2]*(a + b*x)^2,x]
[Out]
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Maple [A] time = 0.007, size = 32, normalized size = 0.6 \[{\frac{{x}^{4} \left ( 15\,{b}^{2}{x}^{2}+35\,abx+21\,{a}^{2} \right ) }{105}\sqrt{c{x}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3*(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^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.199967, size = 45, normalized size = 0.79 \[ \frac{1}{105} \,{\left (15 \, b^{2} x^{6} + 35 \, a b x^{5} + 21 \, a^{2} x^{4}\right )} \sqrt{c x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(c*x^2)*(b*x + a)^2*x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.77094, size = 60, normalized size = 1.05 \[ \frac{a^{2} \sqrt{c} x^{4} \sqrt{x^{2}}}{5} + \frac{a b \sqrt{c} x^{5} \sqrt{x^{2}}}{3} + \frac{b^{2} \sqrt{c} x^{6} \sqrt{x^{2}}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3*(b*x+a)**2*(c*x**2)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.207127, size = 47, normalized size = 0.82 \[ \frac{1}{105} \,{\left (15 \, b^{2} x^{7}{\rm sign}\left (x\right ) + 35 \, a b x^{6}{\rm sign}\left (x\right ) + 21 \, a^{2} x^{5}{\rm sign}\left (x\right )\right )} \sqrt{c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(c*x^2)*(b*x + a)^2*x^3,x, algorithm="giac")
[Out]