Optimal. Leaf size=43 \[ -\frac {a^3}{2 x^2}+\frac {3}{2} a^2 b x^2+\frac {1}{2} a b^2 x^6+\frac {b^3 x^{10}}{10} \]
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Rubi [A]
time = 0.01, antiderivative size = 43, 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}{2 x^2}+\frac {3}{2} a^2 b x^2+\frac {1}{2} a b^2 x^6+\frac {b^3 x^{10}}{10} \end {gather*}
Antiderivative was successfully verified.
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Rule 276
Rubi steps
\begin {align*} \int \frac {\left (a+b x^4\right )^3}{x^3} \, dx &=\int \left (\frac {a^3}{x^3}+3 a^2 b x+3 a b^2 x^5+b^3 x^9\right ) \, dx\\ &=-\frac {a^3}{2 x^2}+\frac {3}{2} a^2 b x^2+\frac {1}{2} a b^2 x^6+\frac {b^3 x^{10}}{10}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 43, normalized size = 1.00 \begin {gather*} -\frac {a^3}{2 x^2}+\frac {3}{2} a^2 b x^2+\frac {1}{2} a b^2 x^6+\frac {b^3 x^{10}}{10} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 36, normalized size = 0.84
method | result | size |
default | \(-\frac {a^{3}}{2 x^{2}}+\frac {3 a^{2} b \,x^{2}}{2}+\frac {a \,b^{2} x^{6}}{2}+\frac {b^{3} x^{10}}{10}\) | \(36\) |
risch | \(-\frac {a^{3}}{2 x^{2}}+\frac {3 a^{2} b \,x^{2}}{2}+\frac {a \,b^{2} x^{6}}{2}+\frac {b^{3} x^{10}}{10}\) | \(36\) |
norman | \(\frac {\frac {1}{10} b^{3} x^{12}+\frac {1}{2} a \,b^{2} x^{8}+\frac {3}{2} a^{2} b \,x^{4}-\frac {1}{2} a^{3}}{x^{2}}\) | \(37\) |
gosper | \(-\frac {-b^{3} x^{12}-5 a \,b^{2} x^{8}-15 a^{2} b \,x^{4}+5 a^{3}}{10 x^{2}}\) | \(38\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 35, normalized size = 0.81 \begin {gather*} \frac {1}{10} \, b^{3} x^{10} + \frac {1}{2} \, a b^{2} x^{6} + \frac {3}{2} \, a^{2} b x^{2} - \frac {a^{3}}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 36, normalized size = 0.84 \begin {gather*} \frac {b^{3} x^{12} + 5 \, a b^{2} x^{8} + 15 \, a^{2} b x^{4} - 5 \, a^{3}}{10 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 37, normalized size = 0.86 \begin {gather*} - \frac {a^{3}}{2 x^{2}} + \frac {3 a^{2} b x^{2}}{2} + \frac {a b^{2} x^{6}}{2} + \frac {b^{3} x^{10}}{10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.56, size = 35, normalized size = 0.81 \begin {gather*} \frac {1}{10} \, b^{3} x^{10} + \frac {1}{2} \, a b^{2} x^{6} + \frac {3}{2} \, a^{2} b x^{2} - \frac {a^{3}}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 35, normalized size = 0.81 \begin {gather*} \frac {b^3\,x^{10}}{10}-\frac {a^3}{2\,x^2}+\frac {3\,a^2\,b\,x^2}{2}+\frac {a\,b^2\,x^6}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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