Optimal. Leaf size=47 \[ -\frac {a^3}{2 x^2}-\frac {9 a^2 b}{7 x^{7/3}}-\frac {9 a b^2}{8 x^{8/3}}-\frac {b^3}{3 x^3} \]
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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} \[ -\frac {9 a^2 b}{7 x^{7/3}}-\frac {a^3}{2 x^2}-\frac {9 a b^2}{8 x^{8/3}}-\frac {b^3}{3 x^3} \]
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 )^3}{x^3} \, dx &=\int \frac {\left (b+a \sqrt [3]{x}\right )^3}{x^4} \, dx\\ &=3 \operatorname {Subst}\left (\int \frac {(b+a x)^3}{x^{10}} \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname {Subst}\left (\int \left (\frac {b^3}{x^{10}}+\frac {3 a b^2}{x^9}+\frac {3 a^2 b}{x^8}+\frac {a^3}{x^7}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=-\frac {b^3}{3 x^3}-\frac {9 a b^2}{8 x^{8/3}}-\frac {9 a^2 b}{7 x^{7/3}}-\frac {a^3}{2 x^2}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 41, normalized size = 0.87 \[ -\frac {84 a^3 x+216 a^2 b x^{2/3}+189 a b^2 \sqrt [3]{x}+56 b^3}{168 x^3} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.72, size = 35, normalized size = 0.74 \[ -\frac {84 \, a^{3} x + 216 \, a^{2} b x^{\frac {2}{3}} + 189 \, a b^{2} x^{\frac {1}{3}} + 56 \, b^{3}}{168 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 35, normalized size = 0.74 \[ -\frac {84 \, a^{3} x + 216 \, a^{2} b x^{\frac {2}{3}} + 189 \, a b^{2} x^{\frac {1}{3}} + 56 \, b^{3}}{168 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 36, normalized size = 0.77 \[ -\frac {a^{3}}{2 x^{2}}-\frac {9 a^{2} b}{7 x^{\frac {7}{3}}}-\frac {9 a \,b^{2}}{8 x^{\frac {8}{3}}}-\frac {b^{3}}{3 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.46, size = 98, normalized size = 2.09 \[ -\frac {{\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{9}}{3 \, b^{6}} + \frac {15 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{8} a}{8 \, b^{6}} - \frac {30 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{7} a^{2}}{7 \, b^{6}} + \frac {5 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{6} a^{3}}{b^{6}} - \frac {3 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{5} a^{4}}{b^{6}} + \frac {3 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{4} a^{5}}{4 \, b^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.12, size = 35, normalized size = 0.74 \[ -\frac {84\,a^3\,x+56\,b^3+189\,a\,b^2\,x^{1/3}+216\,a^2\,b\,x^{2/3}}{168\,x^3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.04, size = 44, normalized size = 0.94 \[ - \frac {a^{3}}{2 x^{2}} - \frac {9 a^{2} b}{7 x^{\frac {7}{3}}} - \frac {9 a b^{2}}{8 x^{\frac {8}{3}}} - \frac {b^{3}}{3 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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