Optimal. Leaf size=120 \[ \frac{15 a^2 \left (a+b \sqrt [3]{x}\right )^{14}}{7 b^6}-\frac{30 a^3 \left (a+b \sqrt [3]{x}\right )^{13}}{13 b^6}+\frac{5 a^4 \left (a+b \sqrt [3]{x}\right )^{12}}{4 b^6}-\frac{3 a^5 \left (a+b \sqrt [3]{x}\right )^{11}}{11 b^6}+\frac{3 \left (a+b \sqrt [3]{x}\right )^{16}}{16 b^6}-\frac{a \left (a+b \sqrt [3]{x}\right )^{15}}{b^6} \]
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Rubi [A] time = 0.065163, antiderivative size = 120, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {266, 43} \[ \frac{15 a^2 \left (a+b \sqrt [3]{x}\right )^{14}}{7 b^6}-\frac{30 a^3 \left (a+b \sqrt [3]{x}\right )^{13}}{13 b^6}+\frac{5 a^4 \left (a+b \sqrt [3]{x}\right )^{12}}{4 b^6}-\frac{3 a^5 \left (a+b \sqrt [3]{x}\right )^{11}}{11 b^6}+\frac{3 \left (a+b \sqrt [3]{x}\right )^{16}}{16 b^6}-\frac{a \left (a+b \sqrt [3]{x}\right )^{15}}{b^6} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \left (a+b \sqrt [3]{x}\right )^{10} x \, dx &=3 \operatorname{Subst}\left (\int x^5 (a+b x)^{10} \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname{Subst}\left (\int \left (-\frac{a^5 (a+b x)^{10}}{b^5}+\frac{5 a^4 (a+b x)^{11}}{b^5}-\frac{10 a^3 (a+b x)^{12}}{b^5}+\frac{10 a^2 (a+b x)^{13}}{b^5}-\frac{5 a (a+b x)^{14}}{b^5}+\frac{(a+b x)^{15}}{b^5}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=-\frac{3 a^5 \left (a+b \sqrt [3]{x}\right )^{11}}{11 b^6}+\frac{5 a^4 \left (a+b \sqrt [3]{x}\right )^{12}}{4 b^6}-\frac{30 a^3 \left (a+b \sqrt [3]{x}\right )^{13}}{13 b^6}+\frac{15 a^2 \left (a+b \sqrt [3]{x}\right )^{14}}{7 b^6}-\frac{a \left (a+b \sqrt [3]{x}\right )^{15}}{b^6}+\frac{3 \left (a+b \sqrt [3]{x}\right )^{16}}{16 b^6}\\ \end{align*}
Mathematica [A] time = 0.0483168, size = 76, normalized size = 0.63 \[ -\frac{\left (a+b \sqrt [3]{x}\right )^{11} \left (66 a^3 b^2 x^{2/3}-286 a^2 b^3 x-11 a^4 b \sqrt [3]{x}+a^5+1001 a b^4 x^{4/3}-3003 b^5 x^{5/3}\right )}{16016 b^6} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 113, normalized size = 0.9 \begin{align*}{\frac{3\,{b}^{10}}{16}{x}^{{\frac{16}{3}}}}+2\,a{b}^{9}{x}^{5}+{\frac{135\,{a}^{2}{b}^{8}}{14}{x}^{{\frac{14}{3}}}}+{\frac{360\,{a}^{3}{b}^{7}}{13}{x}^{{\frac{13}{3}}}}+{\frac{105\,{x}^{4}{a}^{4}{b}^{6}}{2}}+{\frac{756\,{a}^{5}{b}^{5}}{11}{x}^{{\frac{11}{3}}}}+63\,{a}^{6}{b}^{4}{x}^{10/3}+40\,{a}^{7}{b}^{3}{x}^{3}+{\frac{135\,{a}^{8}{b}^{2}}{8}{x}^{{\frac{8}{3}}}}+{\frac{30\,{a}^{9}b}{7}{x}^{{\frac{7}{3}}}}+{\frac{{x}^{2}{a}^{10}}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.96484, size = 132, normalized size = 1.1 \begin{align*} \frac{3 \,{\left (b x^{\frac{1}{3}} + a\right )}^{16}}{16 \, b^{6}} - \frac{{\left (b x^{\frac{1}{3}} + a\right )}^{15} a}{b^{6}} + \frac{15 \,{\left (b x^{\frac{1}{3}} + a\right )}^{14} a^{2}}{7 \, b^{6}} - \frac{30 \,{\left (b x^{\frac{1}{3}} + a\right )}^{13} a^{3}}{13 \, b^{6}} + \frac{5 \,{\left (b x^{\frac{1}{3}} + a\right )}^{12} a^{4}}{4 \, b^{6}} - \frac{3 \,{\left (b x^{\frac{1}{3}} + a\right )}^{11} a^{5}}{11 \, b^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.43978, size = 304, normalized size = 2.53 \begin{align*} 2 \, a b^{9} x^{5} + \frac{105}{2} \, a^{4} b^{6} x^{4} + 40 \, a^{7} b^{3} x^{3} + \frac{1}{2} \, a^{10} x^{2} + \frac{27}{616} \,{\left (220 \, a^{2} b^{8} x^{4} + 1568 \, a^{5} b^{5} x^{3} + 385 \, a^{8} b^{2} x^{2}\right )} x^{\frac{2}{3}} + \frac{3}{1456} \,{\left (91 \, b^{10} x^{5} + 13440 \, a^{3} b^{7} x^{4} + 30576 \, a^{6} b^{4} x^{3} + 2080 \, a^{9} b x^{2}\right )} x^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 3.03308, size = 143, normalized size = 1.19 \begin{align*} \frac{a^{10} x^{2}}{2} + \frac{30 a^{9} b x^{\frac{7}{3}}}{7} + \frac{135 a^{8} b^{2} x^{\frac{8}{3}}}{8} + 40 a^{7} b^{3} x^{3} + 63 a^{6} b^{4} x^{\frac{10}{3}} + \frac{756 a^{5} b^{5} x^{\frac{11}{3}}}{11} + \frac{105 a^{4} b^{6} x^{4}}{2} + \frac{360 a^{3} b^{7} x^{\frac{13}{3}}}{13} + \frac{135 a^{2} b^{8} x^{\frac{14}{3}}}{14} + 2 a b^{9} x^{5} + \frac{3 b^{10} x^{\frac{16}{3}}}{16} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.22985, size = 151, normalized size = 1.26 \begin{align*} \frac{3}{16} \, b^{10} x^{\frac{16}{3}} + 2 \, a b^{9} x^{5} + \frac{135}{14} \, a^{2} b^{8} x^{\frac{14}{3}} + \frac{360}{13} \, a^{3} b^{7} x^{\frac{13}{3}} + \frac{105}{2} \, a^{4} b^{6} x^{4} + \frac{756}{11} \, a^{5} b^{5} x^{\frac{11}{3}} + 63 \, a^{6} b^{4} x^{\frac{10}{3}} + 40 \, a^{7} b^{3} x^{3} + \frac{135}{8} \, a^{8} b^{2} x^{\frac{8}{3}} + \frac{30}{7} \, a^{9} b x^{\frac{7}{3}} + \frac{1}{2} \, a^{10} x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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