Optimal. Leaf size=60 \[ a^2 c x+\frac{1}{2} a^2 d x^2+\frac{1}{2} a b c x^4+\frac{2}{5} a b d x^5+\frac{1}{7} b^2 c x^7+\frac{1}{8} b^2 d x^8 \]
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Rubi [A] time = 0.0713776, antiderivative size = 60, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 28, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.036 \[ a^2 c x+\frac{1}{2} a^2 d x^2+\frac{1}{2} a b c x^4+\frac{2}{5} a b d x^5+\frac{1}{7} b^2 c x^7+\frac{1}{8} b^2 d x^8 \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)*(a*c + a*d*x + b*c*x^3 + b*d*x^4),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ a^{2} d \int x\, dx + a^{2} \int c\, dx + \frac{a b c x^{4}}{2} + \frac{2 a b d x^{5}}{5} + \frac{b^{2} c x^{7}}{7} + \frac{b^{2} d x^{8}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)*(b*d*x**4+b*c*x**3+a*d*x+a*c),x)
[Out]
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Mathematica [A] time = 0.00360621, size = 60, normalized size = 1. \[ a^2 c x+\frac{1}{2} a^2 d x^2+\frac{1}{2} a b c x^4+\frac{2}{5} a b d x^5+\frac{1}{7} b^2 c x^7+\frac{1}{8} b^2 d x^8 \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)*(a*c + a*d*x + b*c*x^3 + b*d*x^4),x]
[Out]
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Maple [A] time = 0.003, size = 51, normalized size = 0.9 \[{a}^{2}cx+{\frac{{a}^{2}d{x}^{2}}{2}}+{\frac{abc{x}^{4}}{2}}+{\frac{2\,abd{x}^{5}}{5}}+{\frac{{b}^{2}c{x}^{7}}{7}}+{\frac{{b}^{2}d{x}^{8}}{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)*(b*d*x^4+b*c*x^3+a*d*x+a*c),x)
[Out]
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Maxima [A] time = 1.44795, size = 68, normalized size = 1.13 \[ \frac{1}{8} \, b^{2} d x^{8} + \frac{1}{7} \, b^{2} c x^{7} + \frac{2}{5} \, a b d x^{5} + \frac{1}{2} \, a b c x^{4} + \frac{1}{2} \, a^{2} d x^{2} + a^{2} c x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*d*x^4 + b*c*x^3 + a*d*x + a*c)*(b*x^3 + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.192193, size = 1, normalized size = 0.02 \[ \frac{1}{8} x^{8} d b^{2} + \frac{1}{7} x^{7} c b^{2} + \frac{2}{5} x^{5} d b a + \frac{1}{2} x^{4} c b a + \frac{1}{2} x^{2} d a^{2} + x c a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*d*x^4 + b*c*x^3 + a*d*x + a*c)*(b*x^3 + a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.055978, size = 58, normalized size = 0.97 \[ a^{2} c x + \frac{a^{2} d x^{2}}{2} + \frac{a b c x^{4}}{2} + \frac{2 a b d x^{5}}{5} + \frac{b^{2} c x^{7}}{7} + \frac{b^{2} d x^{8}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)*(b*d*x**4+b*c*x**3+a*d*x+a*c),x)
[Out]
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GIAC/XCAS [A] time = 0.21294, size = 68, normalized size = 1.13 \[ \frac{1}{8} \, b^{2} d x^{8} + \frac{1}{7} \, b^{2} c x^{7} + \frac{2}{5} \, a b d x^{5} + \frac{1}{2} \, a b c x^{4} + \frac{1}{2} \, a^{2} d x^{2} + a^{2} c x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*d*x^4 + b*c*x^3 + a*d*x + a*c)*(b*x^3 + a),x, algorithm="giac")
[Out]