Optimal. Leaf size=77 \[ -\frac{30 a^3 b^2}{13 x^{13/3}}-\frac{5 a^2 b^3}{2 x^4}-\frac{15 a^4 b}{14 x^{14/3}}-\frac{a^5}{5 x^5}-\frac{15 a b^4}{11 x^{11/3}}-\frac{3 b^5}{10 x^{10/3}} \]
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Rubi [A] time = 0.0337491, antiderivative size = 77, normalized size of antiderivative = 1., 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 266
Rule 43
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*}
Mathematica [A] time = 0.0264998, size = 67, normalized size = 0.87 \[ -\frac{23100 a^3 b^2 x^{2/3}+25025 a^2 b^3 x+10725 a^4 b \sqrt [3]{x}+2002 a^5+13650 a b^4 x^{4/3}+3003 b^5 x^{5/3}}{10010 x^5} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 58, normalized size = 0.8 \begin{align*} -{\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}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.99201, size = 77, normalized size = 1. \begin{align*} -\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}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.61666, size = 162, normalized size = 2.1 \begin{align*} -\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}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 8.99631, size = 76, normalized size = 0.99 \begin{align*} - \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}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.15169, size = 77, normalized size = 1. \begin{align*} -\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}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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