Optimal. Leaf size=17 \[ \frac{a x^4}{4}+\frac{b x^8}{8} \]
[Out]
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Rubi [A] time = 0.0137743, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{a x^4}{4}+\frac{b x^8}{8} \]
Antiderivative was successfully verified.
[In] Int[x^3*(a + b*x^4),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{b \int ^{x^{4}} x\, dx}{4} + \frac{\int ^{x^{4}} a\, dx}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3*(b*x**4+a),x)
[Out]
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Mathematica [A] time = 0.00176247, size = 17, normalized size = 1. \[ \frac{a x^4}{4}+\frac{b x^8}{8} \]
Antiderivative was successfully verified.
[In] Integrate[x^3*(a + b*x^4),x]
[Out]
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Maple [A] time = 0.001, size = 14, normalized size = 0.8 \[{\frac{a{x}^{4}}{4}}+{\frac{b{x}^{8}}{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3*(b*x^4+a),x)
[Out]
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Maxima [A] time = 1.43749, size = 19, normalized size = 1.12 \[ \frac{{\left (b x^{4} + a\right )}^{2}}{8 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)*x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.199839, size = 1, normalized size = 0.06 \[ \frac{1}{8} x^{8} b + \frac{1}{4} x^{4} a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)*x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.066283, size = 12, normalized size = 0.71 \[ \frac{a x^{4}}{4} + \frac{b x^{8}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3*(b*x**4+a),x)
[Out]
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GIAC/XCAS [A] time = 0.215207, size = 18, normalized size = 1.06 \[ \frac{1}{8} \, b x^{8} + \frac{1}{4} \, a x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)*x^3,x, algorithm="giac")
[Out]