Optimal. Leaf size=27 \[ -\frac{a^2}{3 x^3}+2 a b \log (x)+\frac{b^2 x^3}{3} \]
[Out]
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Rubi [A] time = 0.0396798, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ -\frac{a^2}{3 x^3}+2 a b \log (x)+\frac{b^2 x^3}{3} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^2/x^4,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{2}}{3 x^{3}} + \frac{2 a b \log{\left (x^{3} \right )}}{3} + \frac{\int ^{x^{3}} b^{2}\, dx}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**2/x**4,x)
[Out]
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Mathematica [A] time = 0.00138169, size = 27, normalized size = 1. \[ -\frac{a^2}{3 x^3}+2 a b \log (x)+\frac{b^2 x^3}{3} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^2/x^4,x]
[Out]
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Maple [A] time = 0.007, size = 24, normalized size = 0.9 \[ -{\frac{{a}^{2}}{3\,{x}^{3}}}+{\frac{{b}^{2}{x}^{3}}{3}}+2\,ab\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^2/x^4,x)
[Out]
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Maxima [A] time = 1.43302, size = 34, normalized size = 1.26 \[ \frac{1}{3} \, b^{2} x^{3} + \frac{2}{3} \, a b \log \left (x^{3}\right ) - \frac{a^{2}}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^2/x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.255162, size = 36, normalized size = 1.33 \[ \frac{b^{2} x^{6} + 6 \, a b x^{3} \log \left (x\right ) - a^{2}}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^2/x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.21082, size = 24, normalized size = 0.89 \[ - \frac{a^{2}}{3 x^{3}} + 2 a b \log{\left (x \right )} + \frac{b^{2} x^{3}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**2/x**4,x)
[Out]
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GIAC/XCAS [A] time = 0.219086, size = 43, normalized size = 1.59 \[ \frac{1}{3} \, b^{2} x^{3} + 2 \, a b{\rm ln}\left ({\left | x \right |}\right ) - \frac{2 \, a b x^{3} + a^{2}}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^2/x^4,x, algorithm="giac")
[Out]