Optimal. Leaf size=50 \[ a^2 c x+\frac{1}{7} b x^7 (2 a d+b c)+\frac{1}{4} a x^4 (a d+2 b c)+\frac{1}{10} b^2 d x^{10} \]
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Rubi [A] time = 0.0754555, antiderivative size = 50, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ a^2 c x+\frac{1}{7} b x^7 (2 a d+b c)+\frac{1}{4} a x^4 (a d+2 b c)+\frac{1}{10} b^2 d x^{10} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^2*(c + d*x^3),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ a^{2} \int c\, dx + \frac{a x^{4} \left (a d + 2 b c\right )}{4} + \frac{b^{2} d x^{10}}{10} + \frac{b x^{7} \left (2 a d + b c\right )}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**2*(d*x**3+c),x)
[Out]
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Mathematica [A] time = 0.0136847, size = 50, normalized size = 1. \[ a^2 c x+\frac{1}{7} b x^7 (2 a d+b c)+\frac{1}{4} a x^4 (a d+2 b c)+\frac{1}{10} b^2 d x^{10} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^2*(c + d*x^3),x]
[Out]
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Maple [A] time = 0., size = 49, normalized size = 1. \[{\frac{{b}^{2}d{x}^{10}}{10}}+{\frac{ \left ( 2\,abd+{b}^{2}c \right ){x}^{7}}{7}}+{\frac{ \left ({a}^{2}d+2\,abc \right ){x}^{4}}{4}}+{a}^{2}cx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^2*(d*x^3+c),x)
[Out]
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Maxima [A] time = 1.38326, size = 65, normalized size = 1.3 \[ \frac{1}{10} \, b^{2} d x^{10} + \frac{1}{7} \,{\left (b^{2} c + 2 \, a b d\right )} x^{7} + \frac{1}{4} \,{\left (2 \, a b c + a^{2} d\right )} x^{4} + a^{2} c x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^2*(d*x^3 + c),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.179662, size = 1, normalized size = 0.02 \[ \frac{1}{10} x^{10} d b^{2} + \frac{1}{7} x^{7} c b^{2} + \frac{2}{7} x^{7} d b a + \frac{1}{2} x^{4} c b a + \frac{1}{4} x^{4} d a^{2} + x c a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^2*(d*x^3 + c),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.102264, size = 51, normalized size = 1.02 \[ a^{2} c x + \frac{b^{2} d x^{10}}{10} + x^{7} \left (\frac{2 a b d}{7} + \frac{b^{2} c}{7}\right ) + x^{4} \left (\frac{a^{2} d}{4} + \frac{a b c}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**2*(d*x**3+c),x)
[Out]
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GIAC/XCAS [A] time = 0.209987, size = 68, normalized size = 1.36 \[ \frac{1}{10} \, b^{2} d x^{10} + \frac{1}{7} \, b^{2} c x^{7} + \frac{2}{7} \, a b d x^{7} + \frac{1}{2} \, a b c x^{4} + \frac{1}{4} \, a^{2} d x^{4} + a^{2} c x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^2*(d*x^3 + c),x, algorithm="giac")
[Out]