Optimal. Leaf size=39 \[ -\frac {a^3}{5 x^5}-\frac {3 a^2 b}{2 x^2}+3 a b^2 x+\frac {b^3 x^4}{4} \]
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Rubi [A]
time = 0.01, antiderivative size = 39, 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 = {276}
\begin {gather*} -\frac {a^3}{5 x^5}-\frac {3 a^2 b}{2 x^2}+3 a b^2 x+\frac {b^3 x^4}{4} \end {gather*}
Antiderivative was successfully verified.
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Rule 276
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^3}{x^6} \, dx &=\int \left (3 a b^2+\frac {a^3}{x^6}+\frac {3 a^2 b}{x^3}+b^3 x^3\right ) \, dx\\ &=-\frac {a^3}{5 x^5}-\frac {3 a^2 b}{2 x^2}+3 a b^2 x+\frac {b^3 x^4}{4}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 39, normalized size = 1.00 \begin {gather*} -\frac {a^3}{5 x^5}-\frac {3 a^2 b}{2 x^2}+3 a b^2 x+\frac {b^3 x^4}{4} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 34, normalized size = 0.87
method | result | size |
default | \(-\frac {a^{3}}{5 x^{5}}-\frac {3 a^{2} b}{2 x^{2}}+3 a \,b^{2} x +\frac {b^{3} x^{4}}{4}\) | \(34\) |
risch | \(\frac {b^{3} x^{4}}{4}+3 a \,b^{2} x +\frac {-\frac {3}{2} a^{2} b \,x^{3}-\frac {1}{5} a^{3}}{x^{5}}\) | \(36\) |
norman | \(\frac {\frac {1}{4} b^{3} x^{9}+3 a \,b^{2} x^{6}-\frac {3}{2} a^{2} b \,x^{3}-\frac {1}{5} a^{3}}{x^{5}}\) | \(37\) |
gosper | \(-\frac {-5 b^{3} x^{9}-60 a \,b^{2} x^{6}+30 a^{2} b \,x^{3}+4 a^{3}}{20 x^{5}}\) | \(38\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 36, normalized size = 0.92 \begin {gather*} \frac {1}{4} \, b^{3} x^{4} + 3 \, a b^{2} x - \frac {15 \, a^{2} b x^{3} + 2 \, a^{3}}{10 \, x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 37, normalized size = 0.95 \begin {gather*} \frac {5 \, b^{3} x^{9} + 60 \, a b^{2} x^{6} - 30 \, a^{2} b x^{3} - 4 \, a^{3}}{20 \, x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 37, normalized size = 0.95 \begin {gather*} 3 a b^{2} x + \frac {b^{3} x^{4}}{4} + \frac {- 2 a^{3} - 15 a^{2} b x^{3}}{10 x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.15, size = 36, normalized size = 0.92 \begin {gather*} \frac {1}{4} \, b^{3} x^{4} + 3 \, a b^{2} x - \frac {15 \, a^{2} b x^{3} + 2 \, a^{3}}{10 \, x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 36, normalized size = 0.92 \begin {gather*} \frac {b^3\,x^4}{4}-\frac {\frac {a^3}{5}+\frac {3\,b\,a^2\,x^3}{2}}{x^5}+3\,a\,b^2\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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