Optimal. Leaf size=47 \[ -\frac {a^3}{3 x^3}-\frac {9 a^2 b}{10 x^{10/3}}-\frac {9 a b^2}{11 x^{11/3}}-\frac {b^3}{4 x^4} \]
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Rubi [A] time = 0.02, antiderivative size = 47, 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} \[ -\frac {9 a^2 b}{10 x^{10/3}}-\frac {a^3}{3 x^3}-\frac {9 a b^2}{11 x^{11/3}}-\frac {b^3}{4 x^4} \]
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 )^3}{x^4} \, dx &=\int \frac {\left (b+a \sqrt [3]{x}\right )^3}{x^5} \, dx\\ &=3 \operatorname {Subst}\left (\int \frac {(b+a x)^3}{x^{13}} \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname {Subst}\left (\int \left (\frac {b^3}{x^{13}}+\frac {3 a b^2}{x^{12}}+\frac {3 a^2 b}{x^{11}}+\frac {a^3}{x^{10}}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=-\frac {b^3}{4 x^4}-\frac {9 a b^2}{11 x^{11/3}}-\frac {9 a^2 b}{10 x^{10/3}}-\frac {a^3}{3 x^3}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 41, normalized size = 0.87 \[ -\frac {220 a^3 x+594 a^2 b x^{2/3}+540 a b^2 \sqrt [3]{x}+165 b^3}{660 x^4} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.14, size = 35, normalized size = 0.74 \[ -\frac {220 \, a^{3} x + 594 \, a^{2} b x^{\frac {2}{3}} + 540 \, a b^{2} x^{\frac {1}{3}} + 165 \, b^{3}}{660 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 35, normalized size = 0.74 \[ -\frac {220 \, a^{3} x + 594 \, a^{2} b x^{\frac {2}{3}} + 540 \, a b^{2} x^{\frac {1}{3}} + 165 \, b^{3}}{660 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 36, normalized size = 0.77 \[ -\frac {a^{3}}{3 x^{3}}-\frac {9 a^{2} b}{10 x^{\frac {10}{3}}}-\frac {9 a \,b^{2}}{11 x^{\frac {11}{3}}}-\frac {b^{3}}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.49, size = 149, normalized size = 3.17 \[ -\frac {{\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{12}}{4 \, b^{9}} + \frac {24 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{11} a}{11 \, b^{9}} - \frac {42 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{10} a^{2}}{5 \, b^{9}} + \frac {56 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{9} a^{3}}{3 \, b^{9}} - \frac {105 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{8} a^{4}}{4 \, b^{9}} + \frac {24 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{7} a^{5}}{b^{9}} - \frac {14 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{6} a^{6}}{b^{9}} + \frac {24 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{5} a^{7}}{5 \, b^{9}} - \frac {3 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{4} a^{8}}{4 \, b^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 35, normalized size = 0.74 \[ -\frac {220\,a^3\,x+165\,b^3+540\,a\,b^2\,x^{1/3}+594\,a^2\,b\,x^{2/3}}{660\,x^4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 3.47, size = 44, normalized size = 0.94 \[ - \frac {a^{3}}{3 x^{3}} - \frac {9 a^{2} b}{10 x^{\frac {10}{3}}} - \frac {9 a b^{2}}{11 x^{\frac {11}{3}}} - \frac {b^{3}}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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