Optimal. Leaf size=77 \[ -\frac {a^5}{5 x^5}-\frac {15 a^4 b}{14 x^{14/3}}-\frac {30 a^3 b^2}{13 x^{13/3}}-\frac {5 a^2 b^3}{2 x^4}-\frac {15 a b^4}{11 x^{11/3}}-\frac {3 b^5}{10 x^{10/3}} \]
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Rubi [A] time = 0.03, antiderivative size = 77, 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} \[ -\frac {30 a^3 b^2}{13 x^{13/3}}-\frac {5 a^2 b^3}{2 x^4}-\frac {15 a^4 b}{14 x^{14/3}}-\frac {a^5}{5 x^5}-\frac {15 a b^4}{11 x^{11/3}}-\frac {3 b^5}{10 x^{10/3}} \]
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 )^5}{x^6} \, dx &=3 \operatorname {Subst}\left (\int \frac {(a+b x)^5}{x^{16}} \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname {Subst}\left (\int \left (\frac {a^5}{x^{16}}+\frac {5 a^4 b}{x^{15}}+\frac {10 a^3 b^2}{x^{14}}+\frac {10 a^2 b^3}{x^{13}}+\frac {5 a b^4}{x^{12}}+\frac {b^5}{x^{11}}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=-\frac {a^5}{5 x^5}-\frac {15 a^4 b}{14 x^{14/3}}-\frac {30 a^3 b^2}{13 x^{13/3}}-\frac {5 a^2 b^3}{2 x^4}-\frac {15 a b^4}{11 x^{11/3}}-\frac {3 b^5}{10 x^{10/3}}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 67, normalized size = 0.87 \[ -\frac {2002 a^5+10725 a^4 b \sqrt [3]{x}+23100 a^3 b^2 x^{2/3}+25025 a^2 b^3 x+13650 a b^4 x^{4/3}+3003 b^5 x^{5/3}}{10010 x^5} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.67, size = 59, normalized size = 0.77 \[ -\frac {25025 \, a^{2} b^{3} x + 2002 \, a^{5} + 231 \, {\left (13 \, b^{5} x + 100 \, a^{3} b^{2}\right )} x^{\frac {2}{3}} + 975 \, {\left (14 \, a b^{4} x + 11 \, a^{4} b\right )} x^{\frac {1}{3}}}{10010 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 57, normalized size = 0.74 \[ -\frac {3003 \, b^{5} x^{\frac {5}{3}} + 13650 \, a b^{4} x^{\frac {4}{3}} + 25025 \, a^{2} b^{3} x + 23100 \, a^{3} b^{2} x^{\frac {2}{3}} + 10725 \, a^{4} b x^{\frac {1}{3}} + 2002 \, a^{5}}{10010 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 58, normalized size = 0.75 \[ -\frac {3 b^{5}}{10 x^{\frac {10}{3}}}-\frac {15 a \,b^{4}}{11 x^{\frac {11}{3}}}-\frac {5 a^{2} b^{3}}{2 x^{4}}-\frac {30 a^{3} b^{2}}{13 x^{\frac {13}{3}}}-\frac {15 a^{4} b}{14 x^{\frac {14}{3}}}-\frac {a^{5}}{5 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.82, size = 57, normalized size = 0.74 \[ -\frac {3003 \, b^{5} x^{\frac {5}{3}} + 13650 \, a b^{4} x^{\frac {4}{3}} + 25025 \, a^{2} b^{3} x + 23100 \, a^{3} b^{2} x^{\frac {2}{3}} + 10725 \, a^{4} b x^{\frac {1}{3}} + 2002 \, a^{5}}{10010 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 57, normalized size = 0.74 \[ -\frac {\frac {a^5}{5}+\frac {3\,b^5\,x^{5/3}}{10}+\frac {5\,a^2\,b^3\,x}{2}+\frac {15\,a^4\,b\,x^{1/3}}{14}+\frac {15\,a\,b^4\,x^{4/3}}{11}+\frac {30\,a^3\,b^2\,x^{2/3}}{13}}{x^5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 5.35, size = 76, normalized size = 0.99 \[ - \frac {a^{5}}{5 x^{5}} - \frac {15 a^{4} b}{14 x^{\frac {14}{3}}} - \frac {30 a^{3} b^{2}}{13 x^{\frac {13}{3}}} - \frac {5 a^{2} b^{3}}{2 x^{4}} - \frac {15 a b^{4}}{11 x^{\frac {11}{3}}} - \frac {3 b^{5}}{10 x^{\frac {10}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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