Optimal. Leaf size=217 \[ \frac {a^{15} x^6}{6}+\frac {45}{19} a^{14} b x^{19/3}+\frac {63}{4} a^{13} b^2 x^{20/3}+65 a^{12} b^3 x^7+\frac {4095}{22} a^{11} b^4 x^{22/3}+\frac {9009}{23} a^{10} b^5 x^{23/3}+\frac {5005}{8} a^9 b^6 x^8+\frac {3861}{5} a^8 b^7 x^{25/3}+\frac {1485}{2} a^7 b^8 x^{26/3}+\frac {5005}{9} a^6 b^9 x^9+\frac {1287}{4} a^5 b^{10} x^{28/3}+\frac {4095}{29} a^4 b^{11} x^{29/3}+\frac {91}{2} a^3 b^{12} x^{10}+\frac {315}{31} a^2 b^{13} x^{31/3}+\frac {45}{32} a b^{14} x^{32/3}+\frac {b^{15} x^{11}}{11} \]
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Rubi [A] time = 0.17, antiderivative size = 217, 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} \[ \frac {63}{4} a^{13} b^2 x^{20/3}+65 a^{12} b^3 x^7+\frac {4095}{22} a^{11} b^4 x^{22/3}+\frac {9009}{23} a^{10} b^5 x^{23/3}+\frac {5005}{8} a^9 b^6 x^8+\frac {3861}{5} a^8 b^7 x^{25/3}+\frac {1485}{2} a^7 b^8 x^{26/3}+\frac {5005}{9} a^6 b^9 x^9+\frac {1287}{4} a^5 b^{10} x^{28/3}+\frac {4095}{29} a^4 b^{11} x^{29/3}+\frac {91}{2} a^3 b^{12} x^{10}+\frac {315}{31} a^2 b^{13} x^{31/3}+\frac {45}{19} a^{14} b x^{19/3}+\frac {a^{15} x^6}{6}+\frac {45}{32} a b^{14} x^{32/3}+\frac {b^{15} x^{11}}{11} \]
Antiderivative was successfully verified.
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Rule 43
Rule 266
Rubi steps
\begin {align*} \int \left (a+b \sqrt [3]{x}\right )^{15} x^5 \, dx &=3 \operatorname {Subst}\left (\int x^{17} (a+b x)^{15} \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname {Subst}\left (\int \left (a^{15} x^{17}+15 a^{14} b x^{18}+105 a^{13} b^2 x^{19}+455 a^{12} b^3 x^{20}+1365 a^{11} b^4 x^{21}+3003 a^{10} b^5 x^{22}+5005 a^9 b^6 x^{23}+6435 a^8 b^7 x^{24}+6435 a^7 b^8 x^{25}+5005 a^6 b^9 x^{26}+3003 a^5 b^{10} x^{27}+1365 a^4 b^{11} x^{28}+455 a^3 b^{12} x^{29}+105 a^2 b^{13} x^{30}+15 a b^{14} x^{31}+b^{15} x^{32}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=\frac {a^{15} x^6}{6}+\frac {45}{19} a^{14} b x^{19/3}+\frac {63}{4} a^{13} b^2 x^{20/3}+65 a^{12} b^3 x^7+\frac {4095}{22} a^{11} b^4 x^{22/3}+\frac {9009}{23} a^{10} b^5 x^{23/3}+\frac {5005}{8} a^9 b^6 x^8+\frac {3861}{5} a^8 b^7 x^{25/3}+\frac {1485}{2} a^7 b^8 x^{26/3}+\frac {5005}{9} a^6 b^9 x^9+\frac {1287}{4} a^5 b^{10} x^{28/3}+\frac {4095}{29} a^4 b^{11} x^{29/3}+\frac {91}{2} a^3 b^{12} x^{10}+\frac {315}{31} a^2 b^{13} x^{31/3}+\frac {45}{32} a b^{14} x^{32/3}+\frac {b^{15} x^{11}}{11}\\ \end {align*}
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Mathematica [A] time = 0.13, size = 217, normalized size = 1.00 \[ \frac {a^{15} x^6}{6}+\frac {45}{19} a^{14} b x^{19/3}+\frac {63}{4} a^{13} b^2 x^{20/3}+65 a^{12} b^3 x^7+\frac {4095}{22} a^{11} b^4 x^{22/3}+\frac {9009}{23} a^{10} b^5 x^{23/3}+\frac {5005}{8} a^9 b^6 x^8+\frac {3861}{5} a^8 b^7 x^{25/3}+\frac {1485}{2} a^7 b^8 x^{26/3}+\frac {5005}{9} a^6 b^9 x^9+\frac {1287}{4} a^5 b^{10} x^{28/3}+\frac {4095}{29} a^4 b^{11} x^{29/3}+\frac {91}{2} a^3 b^{12} x^{10}+\frac {315}{31} a^2 b^{13} x^{31/3}+\frac {45}{32} a b^{14} x^{32/3}+\frac {b^{15} x^{11}}{11} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.80, size = 179, normalized size = 0.82 \[ \frac {1}{11} \, b^{15} x^{11} + \frac {91}{2} \, a^{3} b^{12} x^{10} + \frac {5005}{9} \, a^{6} b^{9} x^{9} + \frac {5005}{8} \, a^{9} b^{6} x^{8} + 65 \, a^{12} b^{3} x^{7} + \frac {1}{6} \, a^{15} x^{6} + \frac {9}{21344} \, {\left (3335 \, a b^{14} x^{10} + 334880 \, a^{4} b^{11} x^{9} + 1760880 \, a^{7} b^{8} x^{8} + 928928 \, a^{10} b^{5} x^{7} + 37352 \, a^{13} b^{2} x^{6}\right )} x^{\frac {2}{3}} + \frac {9}{129580} \, {\left (146300 \, a^{2} b^{13} x^{10} + 4632485 \, a^{5} b^{10} x^{9} + 11117964 \, a^{8} b^{7} x^{8} + 2679950 \, a^{11} b^{4} x^{7} + 34100 \, a^{14} b x^{6}\right )} x^{\frac {1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 167, normalized size = 0.77 \[ \frac {1}{11} \, b^{15} x^{11} + \frac {45}{32} \, a b^{14} x^{\frac {32}{3}} + \frac {315}{31} \, a^{2} b^{13} x^{\frac {31}{3}} + \frac {91}{2} \, a^{3} b^{12} x^{10} + \frac {4095}{29} \, a^{4} b^{11} x^{\frac {29}{3}} + \frac {1287}{4} \, a^{5} b^{10} x^{\frac {28}{3}} + \frac {5005}{9} \, a^{6} b^{9} x^{9} + \frac {1485}{2} \, a^{7} b^{8} x^{\frac {26}{3}} + \frac {3861}{5} \, a^{8} b^{7} x^{\frac {25}{3}} + \frac {5005}{8} \, a^{9} b^{6} x^{8} + \frac {9009}{23} \, a^{10} b^{5} x^{\frac {23}{3}} + \frac {4095}{22} \, a^{11} b^{4} x^{\frac {22}{3}} + 65 \, a^{12} b^{3} x^{7} + \frac {63}{4} \, a^{13} b^{2} x^{\frac {20}{3}} + \frac {45}{19} \, a^{14} b x^{\frac {19}{3}} + \frac {1}{6} \, a^{15} x^{6} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 168, normalized size = 0.77 \[ \frac {b^{15} x^{11}}{11}+\frac {45 a \,b^{14} x^{\frac {32}{3}}}{32}+\frac {315 a^{2} b^{13} x^{\frac {31}{3}}}{31}+\frac {91 a^{3} b^{12} x^{10}}{2}+\frac {4095 a^{4} b^{11} x^{\frac {29}{3}}}{29}+\frac {1287 a^{5} b^{10} x^{\frac {28}{3}}}{4}+\frac {5005 a^{6} b^{9} x^{9}}{9}+\frac {1485 a^{7} b^{8} x^{\frac {26}{3}}}{2}+\frac {3861 a^{8} b^{7} x^{\frac {25}{3}}}{5}+\frac {5005 a^{9} b^{6} x^{8}}{8}+\frac {9009 a^{10} b^{5} x^{\frac {23}{3}}}{23}+\frac {4095 a^{11} b^{4} x^{\frac {22}{3}}}{22}+65 a^{12} b^{3} x^{7}+\frac {63 a^{13} b^{2} x^{\frac {20}{3}}}{4}+\frac {45 a^{14} b \,x^{\frac {19}{3}}}{19}+\frac {a^{15} x^{6}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.94, size = 302, normalized size = 1.39 \[ \frac {{\left (b x^{\frac {1}{3}} + a\right )}^{33}}{11 \, b^{18}} - \frac {51 \, {\left (b x^{\frac {1}{3}} + a\right )}^{32} a}{32 \, b^{18}} + \frac {408 \, {\left (b x^{\frac {1}{3}} + a\right )}^{31} a^{2}}{31 \, b^{18}} - \frac {68 \, {\left (b x^{\frac {1}{3}} + a\right )}^{30} a^{3}}{b^{18}} + \frac {7140 \, {\left (b x^{\frac {1}{3}} + a\right )}^{29} a^{4}}{29 \, b^{18}} - \frac {663 \, {\left (b x^{\frac {1}{3}} + a\right )}^{28} a^{5}}{b^{18}} + \frac {12376 \, {\left (b x^{\frac {1}{3}} + a\right )}^{27} a^{6}}{9 \, b^{18}} - \frac {2244 \, {\left (b x^{\frac {1}{3}} + a\right )}^{26} a^{7}}{b^{18}} + \frac {14586 \, {\left (b x^{\frac {1}{3}} + a\right )}^{25} a^{8}}{5 \, b^{18}} - \frac {12155 \, {\left (b x^{\frac {1}{3}} + a\right )}^{24} a^{9}}{4 \, b^{18}} + \frac {58344 \, {\left (b x^{\frac {1}{3}} + a\right )}^{23} a^{10}}{23 \, b^{18}} - \frac {18564 \, {\left (b x^{\frac {1}{3}} + a\right )}^{22} a^{11}}{11 \, b^{18}} + \frac {884 \, {\left (b x^{\frac {1}{3}} + a\right )}^{21} a^{12}}{b^{18}} - \frac {357 \, {\left (b x^{\frac {1}{3}} + a\right )}^{20} a^{13}}{b^{18}} + \frac {2040 \, {\left (b x^{\frac {1}{3}} + a\right )}^{19} a^{14}}{19 \, b^{18}} - \frac {68 \, {\left (b x^{\frac {1}{3}} + a\right )}^{18} a^{15}}{3 \, b^{18}} + \frac {3 \, {\left (b x^{\frac {1}{3}} + a\right )}^{17} a^{16}}{b^{18}} - \frac {3 \, {\left (b x^{\frac {1}{3}} + a\right )}^{16} a^{17}}{16 \, b^{18}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.16, size = 167, normalized size = 0.77 \[ \frac {a^{15}\,x^6}{6}+\frac {b^{15}\,x^{11}}{11}+\frac {45\,a^{14}\,b\,x^{19/3}}{19}+\frac {45\,a\,b^{14}\,x^{32/3}}{32}+65\,a^{12}\,b^3\,x^7+\frac {5005\,a^9\,b^6\,x^8}{8}+\frac {5005\,a^6\,b^9\,x^9}{9}+\frac {91\,a^3\,b^{12}\,x^{10}}{2}+\frac {63\,a^{13}\,b^2\,x^{20/3}}{4}+\frac {4095\,a^{11}\,b^4\,x^{22/3}}{22}+\frac {9009\,a^{10}\,b^5\,x^{23/3}}{23}+\frac {3861\,a^8\,b^7\,x^{25/3}}{5}+\frac {1485\,a^7\,b^8\,x^{26/3}}{2}+\frac {1287\,a^5\,b^{10}\,x^{28/3}}{4}+\frac {4095\,a^4\,b^{11}\,x^{29/3}}{29}+\frac {315\,a^2\,b^{13}\,x^{31/3}}{31} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 7.38, size = 218, normalized size = 1.00 \[ \frac {a^{15} x^{6}}{6} + \frac {45 a^{14} b x^{\frac {19}{3}}}{19} + \frac {63 a^{13} b^{2} x^{\frac {20}{3}}}{4} + 65 a^{12} b^{3} x^{7} + \frac {4095 a^{11} b^{4} x^{\frac {22}{3}}}{22} + \frac {9009 a^{10} b^{5} x^{\frac {23}{3}}}{23} + \frac {5005 a^{9} b^{6} x^{8}}{8} + \frac {3861 a^{8} b^{7} x^{\frac {25}{3}}}{5} + \frac {1485 a^{7} b^{8} x^{\frac {26}{3}}}{2} + \frac {5005 a^{6} b^{9} x^{9}}{9} + \frac {1287 a^{5} b^{10} x^{\frac {28}{3}}}{4} + \frac {4095 a^{4} b^{11} x^{\frac {29}{3}}}{29} + \frac {91 a^{3} b^{12} x^{10}}{2} + \frac {315 a^{2} b^{13} x^{\frac {31}{3}}}{31} + \frac {45 a b^{14} x^{\frac {32}{3}}}{32} + \frac {b^{15} x^{11}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
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