Optimal. Leaf size=215 \[ -\frac {a^{15}}{9 x^9}-\frac {45 a^{14} b}{26 x^{26/3}}-\frac {63 a^{13} b^2}{5 x^{25/3}}-\frac {455 a^{12} b^3}{8 x^8}-\frac {4095 a^{11} b^4}{23 x^{23/3}}-\frac {819 a^{10} b^5}{2 x^{22/3}}-\frac {715 a^9 b^6}{x^7}-\frac {3861 a^8 b^7}{4 x^{20/3}}-\frac {19305 a^7 b^8}{19 x^{19/3}}-\frac {5005 a^6 b^9}{6 x^6}-\frac {9009 a^5 b^{10}}{17 x^{17/3}}-\frac {4095 a^4 b^{11}}{16 x^{16/3}}-\frac {91 a^3 b^{12}}{x^5}-\frac {45 a^2 b^{13}}{2 x^{14/3}}-\frac {45 a b^{14}}{13 x^{13/3}}-\frac {b^{15}}{4 x^4} \]
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Rubi [A] time = 0.11, antiderivative size = 215, 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} \[ -\frac {63 a^{13} b^2}{5 x^{25/3}}-\frac {455 a^{12} b^3}{8 x^8}-\frac {4095 a^{11} b^4}{23 x^{23/3}}-\frac {819 a^{10} b^5}{2 x^{22/3}}-\frac {715 a^9 b^6}{x^7}-\frac {3861 a^8 b^7}{4 x^{20/3}}-\frac {19305 a^7 b^8}{19 x^{19/3}}-\frac {5005 a^6 b^9}{6 x^6}-\frac {9009 a^5 b^{10}}{17 x^{17/3}}-\frac {4095 a^4 b^{11}}{16 x^{16/3}}-\frac {91 a^3 b^{12}}{x^5}-\frac {45 a^2 b^{13}}{2 x^{14/3}}-\frac {45 a^{14} b}{26 x^{26/3}}-\frac {a^{15}}{9 x^9}-\frac {45 a b^{14}}{13 x^{13/3}}-\frac {b^{15}}{4 x^4} \]
Antiderivative was successfully verified.
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Rule 43
Rule 266
Rubi steps
\begin {align*} \int \frac {\left (a+b \sqrt [3]{x}\right )^{15}}{x^{10}} \, dx &=3 \operatorname {Subst}\left (\int \frac {(a+b x)^{15}}{x^{28}} \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname {Subst}\left (\int \left (\frac {a^{15}}{x^{28}}+\frac {15 a^{14} b}{x^{27}}+\frac {105 a^{13} b^2}{x^{26}}+\frac {455 a^{12} b^3}{x^{25}}+\frac {1365 a^{11} b^4}{x^{24}}+\frac {3003 a^{10} b^5}{x^{23}}+\frac {5005 a^9 b^6}{x^{22}}+\frac {6435 a^8 b^7}{x^{21}}+\frac {6435 a^7 b^8}{x^{20}}+\frac {5005 a^6 b^9}{x^{19}}+\frac {3003 a^5 b^{10}}{x^{18}}+\frac {1365 a^4 b^{11}}{x^{17}}+\frac {455 a^3 b^{12}}{x^{16}}+\frac {105 a^2 b^{13}}{x^{15}}+\frac {15 a b^{14}}{x^{14}}+\frac {b^{15}}{x^{13}}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=-\frac {a^{15}}{9 x^9}-\frac {45 a^{14} b}{26 x^{26/3}}-\frac {63 a^{13} b^2}{5 x^{25/3}}-\frac {455 a^{12} b^3}{8 x^8}-\frac {4095 a^{11} b^4}{23 x^{23/3}}-\frac {819 a^{10} b^5}{2 x^{22/3}}-\frac {715 a^9 b^6}{x^7}-\frac {3861 a^8 b^7}{4 x^{20/3}}-\frac {19305 a^7 b^8}{19 x^{19/3}}-\frac {5005 a^6 b^9}{6 x^6}-\frac {9009 a^5 b^{10}}{17 x^{17/3}}-\frac {4095 a^4 b^{11}}{16 x^{16/3}}-\frac {91 a^3 b^{12}}{x^5}-\frac {45 a^2 b^{13}}{2 x^{14/3}}-\frac {45 a b^{14}}{13 x^{13/3}}-\frac {b^{15}}{4 x^4}\\ \end {align*}
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Mathematica [A] time = 0.11, size = 215, normalized size = 1.00 \[ -\frac {a^{15}}{9 x^9}-\frac {45 a^{14} b}{26 x^{26/3}}-\frac {63 a^{13} b^2}{5 x^{25/3}}-\frac {455 a^{12} b^3}{8 x^8}-\frac {4095 a^{11} b^4}{23 x^{23/3}}-\frac {819 a^{10} b^5}{2 x^{22/3}}-\frac {715 a^9 b^6}{x^7}-\frac {3861 a^8 b^7}{4 x^{20/3}}-\frac {19305 a^7 b^8}{19 x^{19/3}}-\frac {5005 a^6 b^9}{6 x^6}-\frac {9009 a^5 b^{10}}{17 x^{17/3}}-\frac {4095 a^4 b^{11}}{16 x^{16/3}}-\frac {91 a^3 b^{12}}{x^5}-\frac {45 a^2 b^{13}}{2 x^{14/3}}-\frac {45 a b^{14}}{13 x^{13/3}}-\frac {b^{15}}{4 x^4} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.62, size = 169, normalized size = 0.79 \[ -\frac {17383860 \, b^{15} x^{5} + 6327725040 \, a^{3} b^{12} x^{4} + 58004146200 \, a^{6} b^{9} x^{3} + 49717839600 \, a^{9} b^{6} x^{2} + 3954828150 \, a^{12} b^{3} x + 7726160 \, a^{15} + 31671 \, {\left (7600 \, a b^{14} x^{4} + 561925 \, a^{4} b^{11} x^{3} + 2230800 \, a^{7} b^{8} x^{2} + 899080 \, a^{10} b^{5} x + 27664 \, a^{13} b^{2}\right )} x^{\frac {2}{3}} + 30780 \, {\left (50830 \, a^{2} b^{13} x^{4} + 1197196 \, a^{5} b^{10} x^{3} + 2180607 \, a^{8} b^{7} x^{2} + 402220 \, a^{11} b^{4} x + 3910 \, a^{14} b\right )} x^{\frac {1}{3}}}{69535440 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 167, normalized size = 0.78 \[ -\frac {17383860 \, b^{15} x^{5} + 240699600 \, a b^{14} x^{\frac {14}{3}} + 1564547400 \, a^{2} b^{13} x^{\frac {13}{3}} + 6327725040 \, a^{3} b^{12} x^{4} + 17796726675 \, a^{4} b^{11} x^{\frac {11}{3}} + 36849692880 \, a^{5} b^{10} x^{\frac {10}{3}} + 58004146200 \, a^{6} b^{9} x^{3} + 70651666800 \, a^{7} b^{8} x^{\frac {8}{3}} + 67119083460 \, a^{8} b^{7} x^{\frac {7}{3}} + 49717839600 \, a^{9} b^{6} x^{2} + 28474762680 \, a^{10} b^{5} x^{\frac {5}{3}} + 12380331600 \, a^{11} b^{4} x^{\frac {4}{3}} + 3954828150 \, a^{12} b^{3} x + 876146544 \, a^{13} b^{2} x^{\frac {2}{3}} + 120349800 \, a^{14} b x^{\frac {1}{3}} + 7726160 \, a^{15}}{69535440 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 168, normalized size = 0.78 \[ -\frac {b^{15}}{4 x^{4}}-\frac {45 a \,b^{14}}{13 x^{\frac {13}{3}}}-\frac {45 a^{2} b^{13}}{2 x^{\frac {14}{3}}}-\frac {91 a^{3} b^{12}}{x^{5}}-\frac {4095 a^{4} b^{11}}{16 x^{\frac {16}{3}}}-\frac {9009 a^{5} b^{10}}{17 x^{\frac {17}{3}}}-\frac {5005 a^{6} b^{9}}{6 x^{6}}-\frac {19305 a^{7} b^{8}}{19 x^{\frac {19}{3}}}-\frac {3861 a^{8} b^{7}}{4 x^{\frac {20}{3}}}-\frac {715 a^{9} b^{6}}{x^{7}}-\frac {819 a^{10} b^{5}}{2 x^{\frac {22}{3}}}-\frac {4095 a^{11} b^{4}}{23 x^{\frac {23}{3}}}-\frac {455 a^{12} b^{3}}{8 x^{8}}-\frac {63 a^{13} b^{2}}{5 x^{\frac {25}{3}}}-\frac {45 a^{14} b}{26 x^{\frac {26}{3}}}-\frac {a^{15}}{9 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.79, size = 167, normalized size = 0.78 \[ -\frac {17383860 \, b^{15} x^{5} + 240699600 \, a b^{14} x^{\frac {14}{3}} + 1564547400 \, a^{2} b^{13} x^{\frac {13}{3}} + 6327725040 \, a^{3} b^{12} x^{4} + 17796726675 \, a^{4} b^{11} x^{\frac {11}{3}} + 36849692880 \, a^{5} b^{10} x^{\frac {10}{3}} + 58004146200 \, a^{6} b^{9} x^{3} + 70651666800 \, a^{7} b^{8} x^{\frac {8}{3}} + 67119083460 \, a^{8} b^{7} x^{\frac {7}{3}} + 49717839600 \, a^{9} b^{6} x^{2} + 28474762680 \, a^{10} b^{5} x^{\frac {5}{3}} + 12380331600 \, a^{11} b^{4} x^{\frac {4}{3}} + 3954828150 \, a^{12} b^{3} x + 876146544 \, a^{13} b^{2} x^{\frac {2}{3}} + 120349800 \, a^{14} b x^{\frac {1}{3}} + 7726160 \, a^{15}}{69535440 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.20, size = 167, normalized size = 0.78 \[ -\frac {\frac {a^{15}}{9}+\frac {b^{15}\,x^5}{4}+\frac {455\,a^{12}\,b^3\,x}{8}+\frac {45\,a^{14}\,b\,x^{1/3}}{26}+\frac {45\,a\,b^{14}\,x^{14/3}}{13}+715\,a^9\,b^6\,x^2+\frac {5005\,a^6\,b^9\,x^3}{6}+91\,a^3\,b^{12}\,x^4+\frac {63\,a^{13}\,b^2\,x^{2/3}}{5}+\frac {4095\,a^{11}\,b^4\,x^{4/3}}{23}+\frac {819\,a^{10}\,b^5\,x^{5/3}}{2}+\frac {3861\,a^8\,b^7\,x^{7/3}}{4}+\frac {19305\,a^7\,b^8\,x^{8/3}}{19}+\frac {9009\,a^5\,b^{10}\,x^{10/3}}{17}+\frac {4095\,a^4\,b^{11}\,x^{11/3}}{16}+\frac {45\,a^2\,b^{13}\,x^{13/3}}{2}}{x^9} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 30.92, size = 218, normalized size = 1.01 \[ - \frac {a^{15}}{9 x^{9}} - \frac {45 a^{14} b}{26 x^{\frac {26}{3}}} - \frac {63 a^{13} b^{2}}{5 x^{\frac {25}{3}}} - \frac {455 a^{12} b^{3}}{8 x^{8}} - \frac {4095 a^{11} b^{4}}{23 x^{\frac {23}{3}}} - \frac {819 a^{10} b^{5}}{2 x^{\frac {22}{3}}} - \frac {715 a^{9} b^{6}}{x^{7}} - \frac {3861 a^{8} b^{7}}{4 x^{\frac {20}{3}}} - \frac {19305 a^{7} b^{8}}{19 x^{\frac {19}{3}}} - \frac {5005 a^{6} b^{9}}{6 x^{6}} - \frac {9009 a^{5} b^{10}}{17 x^{\frac {17}{3}}} - \frac {4095 a^{4} b^{11}}{16 x^{\frac {16}{3}}} - \frac {91 a^{3} b^{12}}{x^{5}} - \frac {45 a^{2} b^{13}}{2 x^{\frac {14}{3}}} - \frac {45 a b^{14}}{13 x^{\frac {13}{3}}} - \frac {b^{15}}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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