Optimal. Leaf size=59 \[ \frac{3 a^2 \left (a+b \sqrt [3]{x}\right )^{11}}{11 b^3}+\frac{3 \left (a+b \sqrt [3]{x}\right )^{13}}{13 b^3}-\frac{a \left (a+b \sqrt [3]{x}\right )^{12}}{2 b^3} \]
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Rubi [A] time = 0.0376548, antiderivative size = 59, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182, Rules used = {190, 43} \[ \frac{3 a^2 \left (a+b \sqrt [3]{x}\right )^{11}}{11 b^3}+\frac{3 \left (a+b \sqrt [3]{x}\right )^{13}}{13 b^3}-\frac{a \left (a+b \sqrt [3]{x}\right )^{12}}{2 b^3} \]
Antiderivative was successfully verified.
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Rule 190
Rule 43
Rubi steps
\begin{align*} \int \left (a+b \sqrt [3]{x}\right )^{10} \, dx &=3 \operatorname{Subst}\left (\int x^2 (a+b x)^{10} \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname{Subst}\left (\int \left (\frac{a^2 (a+b x)^{10}}{b^2}-\frac{2 a (a+b x)^{11}}{b^2}+\frac{(a+b x)^{12}}{b^2}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=\frac{3 a^2 \left (a+b \sqrt [3]{x}\right )^{11}}{11 b^3}-\frac{a \left (a+b \sqrt [3]{x}\right )^{12}}{2 b^3}+\frac{3 \left (a+b \sqrt [3]{x}\right )^{13}}{13 b^3}\\ \end{align*}
Mathematica [A] time = 0.0319234, size = 41, normalized size = 0.69 \[ \frac{\left (a+b \sqrt [3]{x}\right )^{11} \left (a^2-11 a b \sqrt [3]{x}+66 b^2 x^{2/3}\right )}{286 b^3} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.002, size = 110, normalized size = 1.9 \begin{align*} x{a}^{10}+{\frac{3\,{b}^{10}}{13}{x}^{{\frac{13}{3}}}}+{\frac{5\,a{b}^{9}{x}^{4}}{2}}+{\frac{135\,{a}^{2}{b}^{8}}{11}{x}^{{\frac{11}{3}}}}+36\,{a}^{3}{b}^{7}{x}^{10/3}+70\,{a}^{4}{b}^{6}{x}^{3}+{\frac{189\,{a}^{5}{b}^{5}}{2}{x}^{{\frac{8}{3}}}}+90\,{a}^{6}{b}^{4}{x}^{7/3}+60\,{a}^{7}{b}^{3}{x}^{2}+27\,{a}^{8}{b}^{2}{x}^{5/3}+{\frac{15\,{a}^{9}b}{2}{x}^{{\frac{4}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.946849, size = 63, normalized size = 1.07 \begin{align*} \frac{3 \,{\left (b x^{\frac{1}{3}} + a\right )}^{13}}{13 \, b^{3}} - \frac{{\left (b x^{\frac{1}{3}} + a\right )}^{12} a}{2 \, b^{3}} + \frac{3 \,{\left (b x^{\frac{1}{3}} + a\right )}^{11} a^{2}}{11 \, b^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.45207, size = 270, normalized size = 4.58 \begin{align*} \frac{5}{2} \, a b^{9} x^{4} + 70 \, a^{4} b^{6} x^{3} + 60 \, a^{7} b^{3} x^{2} + a^{10} x + \frac{27}{22} \,{\left (10 \, a^{2} b^{8} x^{3} + 77 \, a^{5} b^{5} x^{2} + 22 \, a^{8} b^{2} x\right )} x^{\frac{2}{3}} + \frac{3}{26} \,{\left (2 \, b^{10} x^{4} + 312 \, a^{3} b^{7} x^{3} + 780 \, a^{6} b^{4} x^{2} + 65 \, a^{9} b x\right )} x^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 2.63423, size = 136, normalized size = 2.31 \begin{align*} a^{10} x + \frac{15 a^{9} b x^{\frac{4}{3}}}{2} + 27 a^{8} b^{2} x^{\frac{5}{3}} + 60 a^{7} b^{3} x^{2} + 90 a^{6} b^{4} x^{\frac{7}{3}} + \frac{189 a^{5} b^{5} x^{\frac{8}{3}}}{2} + 70 a^{4} b^{6} x^{3} + 36 a^{3} b^{7} x^{\frac{10}{3}} + \frac{135 a^{2} b^{8} x^{\frac{11}{3}}}{11} + \frac{5 a b^{9} x^{4}}{2} + \frac{3 b^{10} x^{\frac{13}{3}}}{13} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.16008, size = 147, normalized size = 2.49 \begin{align*} \frac{3}{13} \, b^{10} x^{\frac{13}{3}} + \frac{5}{2} \, a b^{9} x^{4} + \frac{135}{11} \, a^{2} b^{8} x^{\frac{11}{3}} + 36 \, a^{3} b^{7} x^{\frac{10}{3}} + 70 \, a^{4} b^{6} x^{3} + \frac{189}{2} \, a^{5} b^{5} x^{\frac{8}{3}} + 90 \, a^{6} b^{4} x^{\frac{7}{3}} + 60 \, a^{7} b^{3} x^{2} + 27 \, a^{8} b^{2} x^{\frac{5}{3}} + \frac{15}{2} \, a^{9} b x^{\frac{4}{3}} + a^{10} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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