Optimal. Leaf size=41 \[ -\frac {a^3}{7 x^7}-\frac {3 a^2 b}{4 x^4}-\frac {3 a b^2}{x}+\frac {b^3 x^2}{2} \]
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Rubi [A] time = 0.01, antiderivative size = 41, 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} \[ -\frac {3 a^2 b}{4 x^4}-\frac {a^3}{7 x^7}-\frac {3 a b^2}{x}+\frac {b^3 x^2}{2} \]
Antiderivative was successfully verified.
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Rule 270
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^3}{x^8} \, dx &=\int \left (\frac {a^3}{x^8}+\frac {3 a^2 b}{x^5}+\frac {3 a b^2}{x^2}+b^3 x\right ) \, dx\\ &=-\frac {a^3}{7 x^7}-\frac {3 a^2 b}{4 x^4}-\frac {3 a b^2}{x}+\frac {b^3 x^2}{2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 41, normalized size = 1.00 \[ -\frac {a^3}{7 x^7}-\frac {3 a^2 b}{4 x^4}-\frac {3 a b^2}{x}+\frac {b^3 x^2}{2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.82, size = 37, normalized size = 0.90 \[ \frac {14 \, b^{3} x^{9} - 84 \, a b^{2} x^{6} - 21 \, a^{2} b x^{3} - 4 \, a^{3}}{28 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 38, normalized size = 0.93 \[ \frac {1}{2} \, b^{3} x^{2} - \frac {84 \, a b^{2} x^{6} + 21 \, a^{2} b x^{3} + 4 \, a^{3}}{28 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 36, normalized size = 0.88 \[ \frac {b^{3} x^{2}}{2}-\frac {3 a \,b^{2}}{x}-\frac {3 a^{2} b}{4 x^{4}}-\frac {a^{3}}{7 x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.29, size = 38, normalized size = 0.93 \[ \frac {1}{2} \, b^{3} x^{2} - \frac {84 \, a b^{2} x^{6} + 21 \, a^{2} b x^{3} + 4 \, a^{3}}{28 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.98, size = 38, normalized size = 0.93 \[ \frac {b^3\,x^2}{2}-\frac {\frac {a^3}{7}+\frac {3\,a^2\,b\,x^3}{4}+3\,a\,b^2\,x^6}{x^7} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.28, size = 39, normalized size = 0.95 \[ \frac {b^{3} x^{2}}{2} + \frac {- 4 a^{3} - 21 a^{2} b x^{3} - 84 a b^{2} x^{6}}{28 x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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