Optimal. Leaf size=28 \[ a^2 \log (x)+6 a b \sqrt [3]{x}+\frac {3}{2} b^2 x^{2/3} \]
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Rubi [A] time = 0.01, antiderivative size = 28, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {266, 43} \[ a^2 \log (x)+6 a b \sqrt [3]{x}+\frac {3}{2} b^2 x^{2/3} \]
Antiderivative was successfully verified.
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Rule 43
Rule 266
Rubi steps
\begin {align*} \int \frac {\left (a+b \sqrt [3]{x}\right )^2}{x} \, dx &=3 \operatorname {Subst}\left (\int \frac {(a+b x)^2}{x} \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname {Subst}\left (\int \left (2 a b+\frac {a^2}{x}+b^2 x\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=6 a b \sqrt [3]{x}+\frac {3}{2} b^2 x^{2/3}+a^2 \log (x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 28, normalized size = 1.00 \[ a^2 \log (x)+6 a b \sqrt [3]{x}+\frac {3}{2} b^2 x^{2/3} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 25, normalized size = 0.89 \[ 3 \, a^{2} \log \left (x^{\frac {1}{3}}\right ) + \frac {3}{2} \, b^{2} x^{\frac {2}{3}} + 6 \, a b x^{\frac {1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 23, normalized size = 0.82 \[ a^{2} \log \left ({\left | x \right |}\right ) + \frac {3}{2} \, b^{2} x^{\frac {2}{3}} + 6 \, a b x^{\frac {1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 23, normalized size = 0.82 \[ a^{2} \ln \relax (x )+\frac {3 b^{2} x^{\frac {2}{3}}}{2}+6 a b \,x^{\frac {1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.89, size = 22, normalized size = 0.79 \[ a^{2} \log \relax (x) + \frac {3}{2} \, b^{2} x^{\frac {2}{3}} + 6 \, a b x^{\frac {1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.11, size = 25, normalized size = 0.89 \[ 3\,a^2\,\ln \left (x^{1/3}\right )+\frac {3\,b^2\,x^{2/3}}{2}+6\,a\,b\,x^{1/3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.24, size = 27, normalized size = 0.96 \[ a^{2} \log {\relax (x )} + 6 a b \sqrt [3]{x} + \frac {3 b^{2} x^{\frac {2}{3}}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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