Optimal. Leaf size=19 \[ -\frac {\left (a+b \sqrt [3]{x}\right )^3}{a x} \]
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Rubi [A] time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {264} \[ -\frac {\left (a+b \sqrt [3]{x}\right )^3}{a x} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin {align*} \int \frac {\left (a+b \sqrt [3]{x}\right )^2}{x^2} \, dx &=-\frac {\left (a+b \sqrt [3]{x}\right )^3}{a x}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 19, normalized size = 1.00 \[ -\frac {\left (a+b \sqrt [3]{x}\right )^3}{a x} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.58, size = 24, normalized size = 1.26 \[ -\frac {3 \, b^{2} x^{\frac {2}{3}} + 3 \, a b x^{\frac {1}{3}} + a^{2}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 24, normalized size = 1.26 \[ -\frac {3 \, b^{2} x^{\frac {2}{3}} + 3 \, a b x^{\frac {1}{3}} + a^{2}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 25, normalized size = 1.32 \[ -\frac {3 b^{2}}{x^{\frac {1}{3}}}-\frac {3 a b}{x^{\frac {2}{3}}}-\frac {a^{2}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.93, size = 24, normalized size = 1.26 \[ -\frac {3 \, b^{2} x^{\frac {2}{3}} + 3 \, a b x^{\frac {1}{3}} + a^{2}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 24, normalized size = 1.26 \[ -\frac {a^2}{x}-\frac {3\,b^2}{x^{1/3}}-\frac {3\,a\,b}{x^{2/3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.63, size = 26, normalized size = 1.37 \[ - \frac {a^{2}}{x} - \frac {3 a b}{x^{\frac {2}{3}}} - \frac {3 b^{2}}{\sqrt [3]{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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