Optimal. Leaf size=28 \[ -\frac {a^2}{x}+\frac {2}{3} a b x^3+\frac {b^2 x^7}{7} \]
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Rubi [A] time = 0.01, antiderivative size = 28, 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} \[ -\frac {a^2}{x}+\frac {2}{3} a b x^3+\frac {b^2 x^7}{7} \]
Antiderivative was successfully verified.
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Rule 270
Rubi steps
\begin {align*} \int \frac {\left (a+b x^4\right )^2}{x^2} \, dx &=\int \left (\frac {a^2}{x^2}+2 a b x^2+b^2 x^6\right ) \, dx\\ &=-\frac {a^2}{x}+\frac {2}{3} a b x^3+\frac {b^2 x^7}{7}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 28, normalized size = 1.00 \[ -\frac {a^2}{x}+\frac {2}{3} a b x^3+\frac {b^2 x^7}{7} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.76, size = 26, normalized size = 0.93 \[ \frac {3 \, b^{2} x^{8} + 14 \, a b x^{4} - 21 \, a^{2}}{21 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 24, normalized size = 0.86 \[ \frac {1}{7} \, b^{2} x^{7} + \frac {2}{3} \, a b x^{3} - \frac {a^{2}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 25, normalized size = 0.89 \[ \frac {b^{2} x^{7}}{7}+\frac {2 a b \,x^{3}}{3}-\frac {a^{2}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.30, size = 24, normalized size = 0.86 \[ \frac {1}{7} \, b^{2} x^{7} + \frac {2}{3} \, a b x^{3} - \frac {a^{2}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 25, normalized size = 0.89 \[ \frac {-a^2+\frac {2\,a\,b\,x^4}{3}+\frac {b^2\,x^8}{7}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.20, size = 22, normalized size = 0.79 \[ - \frac {a^{2}}{x} + \frac {2 a b x^{3}}{3} + \frac {b^{2} x^{7}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
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