Optimal. Leaf size=50 \[ \frac{1}{7} d x^7 (a d+2 b c)+\frac{1}{4} c x^4 (2 a d+b c)+a c^2 x+\frac{1}{10} b d^2 x^{10} \]
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Rubi [A] time = 0.0742223, 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 \[ \frac{1}{7} d x^7 (a d+2 b c)+\frac{1}{4} c x^4 (2 a d+b c)+a c^2 x+\frac{1}{10} b d^2 x^{10} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)*(c + d*x^3)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{b d^{2} x^{10}}{10} + c^{2} \int a\, dx + \frac{c x^{4} \left (2 a d + b c\right )}{4} + \frac{d x^{7} \left (a d + 2 b c\right )}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)*(d*x**3+c)**2,x)
[Out]
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Mathematica [A] time = 0.0141192, size = 50, normalized size = 1. \[ \frac{1}{7} d x^7 (a d+2 b c)+\frac{1}{4} c x^4 (2 a d+b c)+a c^2 x+\frac{1}{10} b d^2 x^{10} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)*(c + d*x^3)^2,x]
[Out]
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Maple [A] time = 0.001, size = 49, normalized size = 1. \[{\frac{b{d}^{2}{x}^{10}}{10}}+{\frac{ \left ( a{d}^{2}+2\,bcd \right ){x}^{7}}{7}}+{\frac{ \left ( 2\,acd+b{c}^{2} \right ){x}^{4}}{4}}+a{c}^{2}x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)*(d*x^3+c)^2,x)
[Out]
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Maxima [A] time = 1.36066, size = 65, normalized size = 1.3 \[ \frac{1}{10} \, b d^{2} x^{10} + \frac{1}{7} \,{\left (2 \, b c d + a d^{2}\right )} x^{7} + \frac{1}{4} \,{\left (b c^{2} + 2 \, a c d\right )} x^{4} + a c^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)*(d*x^3 + c)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.180838, size = 1, normalized size = 0.02 \[ \frac{1}{10} x^{10} d^{2} b + \frac{2}{7} x^{7} d c b + \frac{1}{7} x^{7} d^{2} a + \frac{1}{4} x^{4} c^{2} b + \frac{1}{2} x^{4} d c a + x c^{2} a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)*(d*x^3 + c)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.108516, size = 51, normalized size = 1.02 \[ a c^{2} x + \frac{b d^{2} x^{10}}{10} + x^{7} \left (\frac{a d^{2}}{7} + \frac{2 b c d}{7}\right ) + x^{4} \left (\frac{a c d}{2} + \frac{b c^{2}}{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)*(d*x**3+c)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.213265, size = 68, normalized size = 1.36 \[ \frac{1}{10} \, b d^{2} x^{10} + \frac{2}{7} \, b c d x^{7} + \frac{1}{7} \, a d^{2} x^{7} + \frac{1}{4} \, b c^{2} x^{4} + \frac{1}{2} \, a c d x^{4} + a c^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)*(d*x^3 + c)^2,x, algorithm="giac")
[Out]