Optimal. Leaf size=34 \[ \frac {a^3 x^5}{5}+a^2 b x^3+3 a b^2 x-\frac {b^3}{x} \]
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Rubi [A] time = 0.01, antiderivative size = 34, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {263, 270} \[ a^2 b x^3+\frac {a^3 x^5}{5}+3 a b^2 x-\frac {b^3}{x} \]
Antiderivative was successfully verified.
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Rule 263
Rule 270
Rubi steps
\begin {align*} \int \left (a+\frac {b}{x^2}\right )^3 x^4 \, dx &=\int \frac {\left (b+a x^2\right )^3}{x^2} \, dx\\ &=\int \left (3 a b^2+\frac {b^3}{x^2}+3 a^2 b x^2+a^3 x^4\right ) \, dx\\ &=-\frac {b^3}{x}+3 a b^2 x+a^2 b x^3+\frac {a^3 x^5}{5}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 34, normalized size = 1.00 \[ \frac {a^3 x^5}{5}+a^2 b x^3+3 a b^2 x-\frac {b^3}{x} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.53, size = 36, normalized size = 1.06 \[ \frac {a^{3} x^{6} + 5 \, a^{2} b x^{4} + 15 \, a b^{2} x^{2} - 5 \, b^{3}}{5 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 32, normalized size = 0.94 \[ \frac {1}{5} \, a^{3} x^{5} + a^{2} b x^{3} + 3 \, a b^{2} x - \frac {b^{3}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 33, normalized size = 0.97 \[ \frac {a^{3} x^{5}}{5}+a^{2} b \,x^{3}+3 a \,b^{2} x -\frac {b^{3}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.91, size = 32, normalized size = 0.94 \[ \frac {1}{5} \, a^{3} x^{5} + a^{2} b x^{3} + 3 \, a b^{2} x - \frac {b^{3}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 32, normalized size = 0.94 \[ \frac {a^3\,x^5}{5}-\frac {b^3}{x}+a^2\,b\,x^3+3\,a\,b^2\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 29, normalized size = 0.85 \[ \frac {a^{3} x^{5}}{5} + a^{2} b x^{3} + 3 a b^{2} x - \frac {b^{3}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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