Optimal. Leaf size=144 \[ \frac {a^{10} x^5}{5}+\frac {15}{8} a^9 b x^{16/3}+\frac {135}{17} a^8 b^2 x^{17/3}+20 a^7 b^3 x^6+\frac {630}{19} a^6 b^4 x^{19/3}+\frac {189}{5} a^5 b^5 x^{20/3}+30 a^4 b^6 x^7+\frac {180}{11} a^3 b^7 x^{22/3}+\frac {135}{23} a^2 b^8 x^{23/3}+\frac {5}{4} a b^9 x^8+\frac {3}{25} b^{10} x^{25/3} \]
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Rubi [A] time = 0.10, antiderivative size = 144, 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} \[ \frac {135}{17} a^8 b^2 x^{17/3}+20 a^7 b^3 x^6+\frac {630}{19} a^6 b^4 x^{19/3}+\frac {189}{5} a^5 b^5 x^{20/3}+30 a^4 b^6 x^7+\frac {180}{11} a^3 b^7 x^{22/3}+\frac {135}{23} a^2 b^8 x^{23/3}+\frac {15}{8} a^9 b x^{16/3}+\frac {a^{10} x^5}{5}+\frac {5}{4} a b^9 x^8+\frac {3}{25} b^{10} x^{25/3} \]
Antiderivative was successfully verified.
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Rule 43
Rule 266
Rubi steps
\begin {align*} \int \left (a+b \sqrt [3]{x}\right )^{10} x^4 \, dx &=3 \operatorname {Subst}\left (\int x^{14} (a+b x)^{10} \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname {Subst}\left (\int \left (a^{10} x^{14}+10 a^9 b x^{15}+45 a^8 b^2 x^{16}+120 a^7 b^3 x^{17}+210 a^6 b^4 x^{18}+252 a^5 b^5 x^{19}+210 a^4 b^6 x^{20}+120 a^3 b^7 x^{21}+45 a^2 b^8 x^{22}+10 a b^9 x^{23}+b^{10} x^{24}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=\frac {a^{10} x^5}{5}+\frac {15}{8} a^9 b x^{16/3}+\frac {135}{17} a^8 b^2 x^{17/3}+20 a^7 b^3 x^6+\frac {630}{19} a^6 b^4 x^{19/3}+\frac {189}{5} a^5 b^5 x^{20/3}+30 a^4 b^6 x^7+\frac {180}{11} a^3 b^7 x^{22/3}+\frac {135}{23} a^2 b^8 x^{23/3}+\frac {5}{4} a b^9 x^8+\frac {3}{25} b^{10} x^{25/3}\\ \end {align*}
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Mathematica [A] time = 0.11, size = 144, normalized size = 1.00 \[ \frac {a^{10} x^5}{5}+\frac {15}{8} a^9 b x^{16/3}+\frac {135}{17} a^8 b^2 x^{17/3}+20 a^7 b^3 x^6+\frac {630}{19} a^6 b^4 x^{19/3}+\frac {189}{5} a^5 b^5 x^{20/3}+30 a^4 b^6 x^7+\frac {180}{11} a^3 b^7 x^{22/3}+\frac {135}{23} a^2 b^8 x^{23/3}+\frac {5}{4} a b^9 x^8+\frac {3}{25} b^{10} x^{25/3} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.81, size = 124, normalized size = 0.86 \[ \frac {5}{4} \, a b^{9} x^{8} + 30 \, a^{4} b^{6} x^{7} + 20 \, a^{7} b^{3} x^{6} + \frac {1}{5} \, a^{10} x^{5} + \frac {27}{1955} \, {\left (425 \, a^{2} b^{8} x^{7} + 2737 \, a^{5} b^{5} x^{6} + 575 \, a^{8} b^{2} x^{5}\right )} x^{\frac {2}{3}} + \frac {3}{41800} \, {\left (1672 \, b^{10} x^{8} + 228000 \, a^{3} b^{7} x^{7} + 462000 \, a^{6} b^{4} x^{6} + 26125 \, a^{9} b x^{5}\right )} x^{\frac {1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 112, normalized size = 0.78 \[ \frac {3}{25} \, b^{10} x^{\frac {25}{3}} + \frac {5}{4} \, a b^{9} x^{8} + \frac {135}{23} \, a^{2} b^{8} x^{\frac {23}{3}} + \frac {180}{11} \, a^{3} b^{7} x^{\frac {22}{3}} + 30 \, a^{4} b^{6} x^{7} + \frac {189}{5} \, a^{5} b^{5} x^{\frac {20}{3}} + \frac {630}{19} \, a^{6} b^{4} x^{\frac {19}{3}} + 20 \, a^{7} b^{3} x^{6} + \frac {135}{17} \, a^{8} b^{2} x^{\frac {17}{3}} + \frac {15}{8} \, a^{9} b x^{\frac {16}{3}} + \frac {1}{5} \, a^{10} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 113, normalized size = 0.78 \[ \frac {3 b^{10} x^{\frac {25}{3}}}{25}+\frac {5 a \,b^{9} x^{8}}{4}+\frac {135 a^{2} b^{8} x^{\frac {23}{3}}}{23}+\frac {180 a^{3} b^{7} x^{\frac {22}{3}}}{11}+30 a^{4} b^{6} x^{7}+\frac {189 a^{5} b^{5} x^{\frac {20}{3}}}{5}+\frac {630 a^{6} b^{4} x^{\frac {19}{3}}}{19}+20 a^{7} b^{3} x^{6}+\frac {135 a^{8} b^{2} x^{\frac {17}{3}}}{17}+\frac {15 a^{9} b \,x^{\frac {16}{3}}}{8}+\frac {a^{10} x^{5}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.92, size = 251, normalized size = 1.74 \[ \frac {3 \, {\left (b x^{\frac {1}{3}} + a\right )}^{25}}{25 \, b^{15}} - \frac {7 \, {\left (b x^{\frac {1}{3}} + a\right )}^{24} a}{4 \, b^{15}} + \frac {273 \, {\left (b x^{\frac {1}{3}} + a\right )}^{23} a^{2}}{23 \, b^{15}} - \frac {546 \, {\left (b x^{\frac {1}{3}} + a\right )}^{22} a^{3}}{11 \, b^{15}} + \frac {143 \, {\left (b x^{\frac {1}{3}} + a\right )}^{21} a^{4}}{b^{15}} - \frac {3003 \, {\left (b x^{\frac {1}{3}} + a\right )}^{20} a^{5}}{10 \, b^{15}} + \frac {9009 \, {\left (b x^{\frac {1}{3}} + a\right )}^{19} a^{6}}{19 \, b^{15}} - \frac {572 \, {\left (b x^{\frac {1}{3}} + a\right )}^{18} a^{7}}{b^{15}} + \frac {9009 \, {\left (b x^{\frac {1}{3}} + a\right )}^{17} a^{8}}{17 \, b^{15}} - \frac {3003 \, {\left (b x^{\frac {1}{3}} + a\right )}^{16} a^{9}}{8 \, b^{15}} + \frac {1001 \, {\left (b x^{\frac {1}{3}} + a\right )}^{15} a^{10}}{5 \, b^{15}} - \frac {78 \, {\left (b x^{\frac {1}{3}} + a\right )}^{14} a^{11}}{b^{15}} + \frac {21 \, {\left (b x^{\frac {1}{3}} + a\right )}^{13} a^{12}}{b^{15}} - \frac {7 \, {\left (b x^{\frac {1}{3}} + a\right )}^{12} a^{13}}{2 \, b^{15}} + \frac {3 \, {\left (b x^{\frac {1}{3}} + a\right )}^{11} a^{14}}{11 \, b^{15}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.15, size = 112, normalized size = 0.78 \[ \frac {a^{10}\,x^5}{5}+\frac {3\,b^{10}\,x^{25/3}}{25}+\frac {5\,a\,b^9\,x^8}{4}+\frac {15\,a^9\,b\,x^{16/3}}{8}+20\,a^7\,b^3\,x^6+30\,a^4\,b^6\,x^7+\frac {135\,a^8\,b^2\,x^{17/3}}{17}+\frac {630\,a^6\,b^4\,x^{19/3}}{19}+\frac {189\,a^5\,b^5\,x^{20/3}}{5}+\frac {180\,a^3\,b^7\,x^{22/3}}{11}+\frac {135\,a^2\,b^8\,x^{23/3}}{23} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 4.67, size = 144, normalized size = 1.00 \[ \frac {a^{10} x^{5}}{5} + \frac {15 a^{9} b x^{\frac {16}{3}}}{8} + \frac {135 a^{8} b^{2} x^{\frac {17}{3}}}{17} + 20 a^{7} b^{3} x^{6} + \frac {630 a^{6} b^{4} x^{\frac {19}{3}}}{19} + \frac {189 a^{5} b^{5} x^{\frac {20}{3}}}{5} + 30 a^{4} b^{6} x^{7} + \frac {180 a^{3} b^{7} x^{\frac {22}{3}}}{11} + \frac {135 a^{2} b^{8} x^{\frac {23}{3}}}{23} + \frac {5 a b^{9} x^{8}}{4} + \frac {3 b^{10} x^{\frac {25}{3}}}{25} \]
Verification of antiderivative is not currently implemented for this CAS.
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