Optimal. Leaf size=26 \[ \frac {2}{3} a b x^3+\frac {b^2 x^6}{6}+a^2 \log (x) \]
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Rubi [A]
time = 0.01, antiderivative size = 26, 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*} a^2 \log (x)+\frac {2}{3} a b x^3+\frac {b^2 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 )^2}{x} \, dx &=\frac {1}{3} \text {Subst}\left (\int \frac {(a+b x)^2}{x} \, dx,x,x^3\right )\\ &=\frac {1}{3} \text {Subst}\left (\int \left (2 a b+\frac {a^2}{x}+b^2 x\right ) \, dx,x,x^3\right )\\ &=\frac {2}{3} a b x^3+\frac {b^2 x^6}{6}+a^2 \log (x)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 26, normalized size = 1.00 \begin {gather*} \frac {2}{3} a b x^3+\frac {b^2 x^6}{6}+a^2 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.14, size = 23, normalized size = 0.88
method | result | size |
default | \(\frac {2 a b \,x^{3}}{3}+\frac {b^{2} x^{6}}{6}+a^{2} \ln \left (x \right )\) | \(23\) |
norman | \(\frac {2 a b \,x^{3}}{3}+\frac {b^{2} x^{6}}{6}+a^{2} \ln \left (x \right )\) | \(23\) |
risch | \(\frac {b^{2} x^{6}}{6}+\frac {2 a b \,x^{3}}{3}+\frac {2 a^{2}}{3}+a^{2} \ln \left (x \right )\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 25, normalized size = 0.96 \begin {gather*} \frac {1}{6} \, b^{2} x^{6} + \frac {2}{3} \, a b x^{3} + \frac {1}{3} \, a^{2} \log \left (x^{3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 22, normalized size = 0.85 \begin {gather*} \frac {1}{6} \, b^{2} x^{6} + \frac {2}{3} \, a b x^{3} + a^{2} \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 24, normalized size = 0.92 \begin {gather*} a^{2} \log {\left (x \right )} + \frac {2 a b x^{3}}{3} + \frac {b^{2} x^{6}}{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.93, size = 23, normalized size = 0.88 \begin {gather*} \frac {1}{6} \, b^{2} x^{6} + \frac {2}{3} \, a b x^{3} + a^{2} \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 22, normalized size = 0.85 \begin {gather*} a^2\,\ln \left (x\right )+\frac {b^2\,x^6}{6}+\frac {2\,a\,b\,x^3}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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