Optimal. Leaf size=27 \[ -\frac {a^2}{2 x^2}+a b x^2+\frac {b^2 x^6}{6} \]
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Rubi [A] time = 0.01, antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {270} \[ -\frac {a^2}{2 x^2}+a b x^2+\frac {b^2 x^6}{6} \]
Antiderivative was successfully verified.
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Rule 270
Rubi steps
\begin {align*} \int \frac {\left (a+b x^4\right )^2}{x^3} \, dx &=\int \left (\frac {a^2}{x^3}+2 a b x+b^2 x^5\right ) \, dx\\ &=-\frac {a^2}{2 x^2}+a b x^2+\frac {b^2 x^6}{6}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 27, normalized size = 1.00 \[ -\frac {a^2}{2 x^2}+a b x^2+\frac {b^2 x^6}{6} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.81, size = 25, normalized size = 0.93 \[ \frac {b^{2} x^{8} + 6 \, a b x^{4} - 3 \, a^{2}}{6 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 23, normalized size = 0.85 \[ \frac {1}{6} \, b^{2} x^{6} + a b x^{2} - \frac {a^{2}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 24, normalized size = 0.89 \[ \frac {b^{2} x^{6}}{6}+a b \,x^{2}-\frac {a^{2}}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.32, size = 23, normalized size = 0.85 \[ \frac {1}{6} \, b^{2} x^{6} + a b x^{2} - \frac {a^{2}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 25, normalized size = 0.93 \[ \frac {-3\,a^2+6\,a\,b\,x^4+b^2\,x^8}{6\,x^2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 22, normalized size = 0.81 \[ - \frac {a^{2}}{2 x^{2}} + a b x^{2} + \frac {b^{2} x^{6}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
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