Optimal. Leaf size=37 \[ -\frac {a^3}{3 x^3}+a b^2 x^3+\frac {b^3 x^6}{6}+3 a^2 b \log (x) \]
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Rubi [A]
time = 0.02, antiderivative size = 37, 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}{3 x^3}+3 a^2 b \log (x)+a b^2 x^3+\frac {b^3 x^6}{6} \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^4} \, dx &=\frac {1}{3} \text {Subst}\left (\int \frac {(a+b x)^3}{x^2} \, dx,x,x^3\right )\\ &=\frac {1}{3} \text {Subst}\left (\int \left (3 a b^2+\frac {a^3}{x^2}+\frac {3 a^2 b}{x}+b^3 x\right ) \, dx,x,x^3\right )\\ &=-\frac {a^3}{3 x^3}+a b^2 x^3+\frac {b^3 x^6}{6}+3 a^2 b \log (x)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 37, normalized size = 1.00 \begin {gather*} -\frac {a^3}{3 x^3}+a b^2 x^3+\frac {b^3 x^6}{6}+3 a^2 b \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.14, size = 34, normalized size = 0.92
method | result | size |
default | \(-\frac {a^{3}}{3 x^{3}}+a \,b^{2} x^{3}+\frac {b^{3} x^{6}}{6}+3 a^{2} b \ln \left (x \right )\) | \(34\) |
norman | \(\frac {a \,b^{2} x^{6}-\frac {1}{3} a^{3}+\frac {1}{6} b^{3} x^{9}}{x^{3}}+3 a^{2} b \ln \left (x \right )\) | \(36\) |
risch | \(\frac {b^{3} x^{6}}{6}+a \,b^{2} x^{3}+\frac {3 a^{2} b}{2}-\frac {a^{3}}{3 x^{3}}+3 a^{2} b \ln \left (x \right )\) | \(40\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 34, normalized size = 0.92 \begin {gather*} \frac {1}{6} \, b^{3} x^{6} + a b^{2} x^{3} + a^{2} b \log \left (x^{3}\right ) - \frac {a^{3}}{3 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 38, normalized size = 1.03 \begin {gather*} \frac {b^{3} x^{9} + 6 \, a b^{2} x^{6} + 18 \, a^{2} b x^{3} \log \left (x\right ) - 2 \, a^{3}}{6 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 34, normalized size = 0.92 \begin {gather*} - \frac {a^{3}}{3 x^{3}} + 3 a^{2} b \log {\left (x \right )} + a b^{2} x^{3} + \frac {b^{3} x^{6}}{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.18, size = 44, normalized size = 1.19 \begin {gather*} \frac {1}{6} \, b^{3} x^{6} + a b^{2} x^{3} + 3 \, a^{2} b \log \left ({\left | x \right |}\right ) - \frac {3 \, a^{2} b x^{3} + a^{3}}{3 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 33, normalized size = 0.89 \begin {gather*} \frac {b^3\,x^6}{6}-\frac {a^3}{3\,x^3}+a\,b^2\,x^3+3\,a^2\,b\,\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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