Optimal. Leaf size=34 \[ -\frac {a^2}{3 x^3}-\frac {3 a b}{5 x^{10/3}}-\frac {3 b^2}{11 x^{11/3}} \]
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Rubi [A] time = 0.02, antiderivative size = 34, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {263, 266, 43} \[ -\frac {a^2}{3 x^3}-\frac {3 a b}{5 x^{10/3}}-\frac {3 b^2}{11 x^{11/3}} \]
Antiderivative was successfully verified.
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Rule 43
Rule 263
Rule 266
Rubi steps
\begin {align*} \int \frac {\left (a+\frac {b}{\sqrt [3]{x}}\right )^2}{x^4} \, dx &=\int \frac {\left (b+a \sqrt [3]{x}\right )^2}{x^{14/3}} \, dx\\ &=3 \operatorname {Subst}\left (\int \frac {(b+a x)^2}{x^{12}} \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname {Subst}\left (\int \left (\frac {b^2}{x^{12}}+\frac {2 a b}{x^{11}}+\frac {a^2}{x^{10}}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=-\frac {3 b^2}{11 x^{11/3}}-\frac {3 a b}{5 x^{10/3}}-\frac {a^2}{3 x^3}\\ \end {align*}
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Mathematica [A] time = 0.04, size = 34, normalized size = 1.00 \[ -\frac {a^2}{3 x^3}-\frac {3 a b}{5 x^{10/3}}-\frac {3 b^2}{11 x^{11/3}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.79, size = 27, normalized size = 0.79 \[ -\frac {55 \, a^{2} x + 99 \, a b x^{\frac {2}{3}} + 45 \, b^{2} x^{\frac {1}{3}}}{165 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 26, normalized size = 0.76 \[ -\frac {55 \, a^{2} x^{\frac {2}{3}} + 99 \, a b x^{\frac {1}{3}} + 45 \, b^{2}}{165 \, x^{\frac {11}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 25, normalized size = 0.74 \[ -\frac {a^{2}}{3 x^{3}}-\frac {3 a b}{5 x^{\frac {10}{3}}}-\frac {3 b^{2}}{11 x^{\frac {11}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.53, size = 149, normalized size = 4.38 \[ -\frac {3 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{11}}{11 \, b^{9}} + \frac {12 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{10} a}{5 \, b^{9}} - \frac {28 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{9} a^{2}}{3 \, b^{9}} + \frac {21 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{8} a^{3}}{b^{9}} - \frac {30 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{7} a^{4}}{b^{9}} + \frac {28 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{6} a^{5}}{b^{9}} - \frac {84 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{5} a^{6}}{5 \, b^{9}} + \frac {6 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{4} a^{7}}{b^{9}} - \frac {{\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{3} a^{8}}{b^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.13, size = 24, normalized size = 0.71 \[ -\frac {a^2}{3\,x^3}-\frac {3\,b^2}{11\,x^{11/3}}-\frac {3\,a\,b}{5\,x^{10/3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.98, size = 32, normalized size = 0.94 \[ - \frac {a^{2}}{3 x^{3}} - \frac {3 a b}{5 x^{\frac {10}{3}}} - \frac {3 b^{2}}{11 x^{\frac {11}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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