Optimal. Leaf size=38 \[ -\frac {a^3}{6 x^6}-\frac {a^2 b}{x^3}+\frac {b^3 x^3}{3}+3 a b^2 \log (x) \]
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Rubi [A]
time = 0.01, antiderivative size = 38, 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 = {272, 45}
\begin {gather*} -\frac {a^3}{6 x^6}-\frac {a^2 b}{x^3}+3 a b^2 \log (x)+\frac {b^3 x^3}{3} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rule 272
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^3}{x^7} \, dx &=\frac {1}{3} \text {Subst}\left (\int \frac {(a+b x)^3}{x^3} \, dx,x,x^3\right )\\ &=\frac {1}{3} \text {Subst}\left (\int \left (b^3+\frac {a^3}{x^3}+\frac {3 a^2 b}{x^2}+\frac {3 a b^2}{x}\right ) \, dx,x,x^3\right )\\ &=-\frac {a^3}{6 x^6}-\frac {a^2 b}{x^3}+\frac {b^3 x^3}{3}+3 a b^2 \log (x)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 38, normalized size = 1.00 \begin {gather*} -\frac {a^3}{6 x^6}-\frac {a^2 b}{x^3}+\frac {b^3 x^3}{3}+3 a b^2 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 35, normalized size = 0.92
method | result | size |
default | \(-\frac {a^{3}}{6 x^{6}}-\frac {a^{2} b}{x^{3}}+\frac {b^{3} x^{3}}{3}+3 a \,b^{2} \ln \left (x \right )\) | \(35\) |
norman | \(\frac {-\frac {1}{6} a^{3}+\frac {1}{3} b^{3} x^{9}-a^{2} b \,x^{3}}{x^{6}}+3 a \,b^{2} \ln \left (x \right )\) | \(37\) |
risch | \(\frac {b^{3} x^{3}}{3}+\frac {-a^{2} b \,x^{3}-\frac {1}{6} a^{3}}{x^{6}}+3 a \,b^{2} \ln \left (x \right )\) | \(37\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 36, normalized size = 0.95 \begin {gather*} \frac {1}{3} \, b^{3} x^{3} + a b^{2} \log \left (x^{3}\right ) - \frac {6 \, a^{2} b x^{3} + a^{3}}{6 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 39, normalized size = 1.03 \begin {gather*} \frac {2 \, b^{3} x^{9} + 18 \, a b^{2} x^{6} \log \left (x\right ) - 6 \, a^{2} b x^{3} - a^{3}}{6 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 37, normalized size = 0.97 \begin {gather*} 3 a b^{2} \log {\left (x \right )} + \frac {b^{3} x^{3}}{3} + \frac {- a^{3} - 6 a^{2} b x^{3}}{6 x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.02, size = 45, normalized size = 1.18 \begin {gather*} \frac {1}{3} \, b^{3} x^{3} + 3 \, a b^{2} \log \left ({\left | x \right |}\right ) - \frac {9 \, a b^{2} x^{6} + 6 \, a^{2} b x^{3} + a^{3}}{6 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.94, size = 36, normalized size = 0.95 \begin {gather*} \frac {b^3\,x^3}{3}-\frac {\frac {a^3}{6}+b\,a^2\,x^3}{x^6}+3\,a\,b^2\,\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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