Optimal. Leaf size=38 \[ -\frac {a^3}{x}+a^2 b x^3+\frac {3}{7} a b^2 x^7+\frac {b^3 x^{11}}{11} \]
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Rubi [A] time = 0.01, antiderivative size = 38, 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} \[ a^2 b x^3-\frac {a^3}{x}+\frac {3}{7} a b^2 x^7+\frac {b^3 x^{11}}{11} \]
Antiderivative was successfully verified.
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Rule 270
Rubi steps
\begin {align*} \int \frac {\left (a+b x^4\right )^3}{x^2} \, dx &=\int \left (\frac {a^3}{x^2}+3 a^2 b x^2+3 a b^2 x^6+b^3 x^{10}\right ) \, dx\\ &=-\frac {a^3}{x}+a^2 b x^3+\frac {3}{7} a b^2 x^7+\frac {b^3 x^{11}}{11}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 38, normalized size = 1.00 \[ -\frac {a^3}{x}+a^2 b x^3+\frac {3}{7} a b^2 x^7+\frac {b^3 x^{11}}{11} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.57, size = 37, normalized size = 0.97 \[ \frac {7 \, b^{3} x^{12} + 33 \, a b^{2} x^{8} + 77 \, a^{2} b x^{4} - 77 \, a^{3}}{77 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.23, size = 34, normalized size = 0.89 \[ \frac {1}{11} \, b^{3} x^{11} + \frac {3}{7} \, a b^{2} x^{7} + a^{2} b x^{3} - \frac {a^{3}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 35, normalized size = 0.92 \[ \frac {b^{3} x^{11}}{11}+\frac {3 a \,b^{2} x^{7}}{7}+a^{2} b \,x^{3}-\frac {a^{3}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.27, size = 34, normalized size = 0.89 \[ \frac {1}{11} \, b^{3} x^{11} + \frac {3}{7} \, a b^{2} x^{7} + a^{2} b x^{3} - \frac {a^{3}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 34, normalized size = 0.89 \[ \frac {b^3\,x^{11}}{11}-\frac {a^3}{x}+a^2\,b\,x^3+\frac {3\,a\,b^2\,x^7}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 32, normalized size = 0.84 \[ - \frac {a^{3}}{x} + a^{2} b x^{3} + \frac {3 a b^{2} x^{7}}{7} + \frac {b^{3} x^{11}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
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