Optimal. Leaf size=142 \[ -\frac {a^{10}}{9 x^9}-\frac {15 a^9 b}{13 x^{26/3}}-\frac {27 a^8 b^2}{5 x^{25/3}}-\frac {15 a^7 b^3}{x^8}-\frac {630 a^6 b^4}{23 x^{23/3}}-\frac {378 a^5 b^5}{11 x^{22/3}}-\frac {30 a^4 b^6}{x^7}-\frac {18 a^3 b^7}{x^{20/3}}-\frac {135 a^2 b^8}{19 x^{19/3}}-\frac {5 a b^9}{3 x^6}-\frac {3 b^{10}}{17 x^{17/3}} \]
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Rubi [A] time = 0.07, antiderivative size = 142, 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} \[ -\frac {27 a^8 b^2}{5 x^{25/3}}-\frac {15 a^7 b^3}{x^8}-\frac {630 a^6 b^4}{23 x^{23/3}}-\frac {378 a^5 b^5}{11 x^{22/3}}-\frac {30 a^4 b^6}{x^7}-\frac {18 a^3 b^7}{x^{20/3}}-\frac {135 a^2 b^8}{19 x^{19/3}}-\frac {15 a^9 b}{13 x^{26/3}}-\frac {a^{10}}{9 x^9}-\frac {5 a b^9}{3 x^6}-\frac {3 b^{10}}{17 x^{17/3}} \]
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 )^{10}}{x^{10}} \, dx &=3 \operatorname {Subst}\left (\int \frac {(a+b x)^{10}}{x^{28}} \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname {Subst}\left (\int \left (\frac {a^{10}}{x^{28}}+\frac {10 a^9 b}{x^{27}}+\frac {45 a^8 b^2}{x^{26}}+\frac {120 a^7 b^3}{x^{25}}+\frac {210 a^6 b^4}{x^{24}}+\frac {252 a^5 b^5}{x^{23}}+\frac {210 a^4 b^6}{x^{22}}+\frac {120 a^3 b^7}{x^{21}}+\frac {45 a^2 b^8}{x^{20}}+\frac {10 a b^9}{x^{19}}+\frac {b^{10}}{x^{18}}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=-\frac {a^{10}}{9 x^9}-\frac {15 a^9 b}{13 x^{26/3}}-\frac {27 a^8 b^2}{5 x^{25/3}}-\frac {15 a^7 b^3}{x^8}-\frac {630 a^6 b^4}{23 x^{23/3}}-\frac {378 a^5 b^5}{11 x^{22/3}}-\frac {30 a^4 b^6}{x^7}-\frac {18 a^3 b^7}{x^{20/3}}-\frac {135 a^2 b^8}{19 x^{19/3}}-\frac {5 a b^9}{3 x^6}-\frac {3 b^{10}}{17 x^{17/3}}\\ \end {align*}
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Mathematica [A] time = 0.06, size = 142, normalized size = 1.00 \[ -\frac {a^{10}}{9 x^9}-\frac {15 a^9 b}{13 x^{26/3}}-\frac {27 a^8 b^2}{5 x^{25/3}}-\frac {15 a^7 b^3}{x^8}-\frac {630 a^6 b^4}{23 x^{23/3}}-\frac {378 a^5 b^5}{11 x^{22/3}}-\frac {30 a^4 b^6}{x^7}-\frac {18 a^3 b^7}{x^{20/3}}-\frac {135 a^2 b^8}{19 x^{19/3}}-\frac {5 a b^9}{3 x^6}-\frac {3 b^{10}}{17 x^{17/3}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.93, size = 114, normalized size = 0.80 \[ -\frac {79676025 \, a b^{9} x^{3} + 1434168450 \, a^{4} b^{6} x^{2} + 717084225 \, a^{7} b^{3} x + 5311735 \, a^{10} + 1235169 \, {\left (275 \, a^{2} b^{8} x^{2} + 1330 \, a^{5} b^{5} x + 209 \, a^{8} b^{2}\right )} x^{\frac {2}{3}} + 28215 \, {\left (299 \, b^{10} x^{3} + 30498 \, a^{3} b^{7} x^{2} + 46410 \, a^{6} b^{4} x + 1955 \, a^{9} b\right )} x^{\frac {1}{3}}}{47805615 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 112, normalized size = 0.79 \[ -\frac {8436285 \, b^{10} x^{\frac {10}{3}} + 79676025 \, a b^{9} x^{3} + 339671475 \, a^{2} b^{8} x^{\frac {8}{3}} + 860501070 \, a^{3} b^{7} x^{\frac {7}{3}} + 1434168450 \, a^{4} b^{6} x^{2} + 1642774770 \, a^{5} b^{5} x^{\frac {5}{3}} + 1309458150 \, a^{6} b^{4} x^{\frac {4}{3}} + 717084225 \, a^{7} b^{3} x + 258150321 \, a^{8} b^{2} x^{\frac {2}{3}} + 55160325 \, a^{9} b x^{\frac {1}{3}} + 5311735 \, a^{10}}{47805615 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 113, normalized size = 0.80 \[ -\frac {3 b^{10}}{17 x^{\frac {17}{3}}}-\frac {5 a \,b^{9}}{3 x^{6}}-\frac {135 a^{2} b^{8}}{19 x^{\frac {19}{3}}}-\frac {18 a^{3} b^{7}}{x^{\frac {20}{3}}}-\frac {30 a^{4} b^{6}}{x^{7}}-\frac {378 a^{5} b^{5}}{11 x^{\frac {22}{3}}}-\frac {630 a^{6} b^{4}}{23 x^{\frac {23}{3}}}-\frac {15 a^{7} b^{3}}{x^{8}}-\frac {27 a^{8} b^{2}}{5 x^{\frac {25}{3}}}-\frac {15 a^{9} b}{13 x^{\frac {26}{3}}}-\frac {a^{10}}{9 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.84, size = 112, normalized size = 0.79 \[ -\frac {8436285 \, b^{10} x^{\frac {10}{3}} + 79676025 \, a b^{9} x^{3} + 339671475 \, a^{2} b^{8} x^{\frac {8}{3}} + 860501070 \, a^{3} b^{7} x^{\frac {7}{3}} + 1434168450 \, a^{4} b^{6} x^{2} + 1642774770 \, a^{5} b^{5} x^{\frac {5}{3}} + 1309458150 \, a^{6} b^{4} x^{\frac {4}{3}} + 717084225 \, a^{7} b^{3} x + 258150321 \, a^{8} b^{2} x^{\frac {2}{3}} + 55160325 \, a^{9} b x^{\frac {1}{3}} + 5311735 \, a^{10}}{47805615 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.19, size = 112, normalized size = 0.79 \[ -\frac {\frac {a^{10}}{9}+\frac {3\,b^{10}\,x^{10/3}}{17}+15\,a^7\,b^3\,x+\frac {5\,a\,b^9\,x^3}{3}+\frac {15\,a^9\,b\,x^{1/3}}{13}+30\,a^4\,b^6\,x^2+\frac {27\,a^8\,b^2\,x^{2/3}}{5}+\frac {630\,a^6\,b^4\,x^{4/3}}{23}+\frac {378\,a^5\,b^5\,x^{5/3}}{11}+18\,a^3\,b^7\,x^{7/3}+\frac {135\,a^2\,b^8\,x^{8/3}}{19}}{x^9} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 27.84, size = 144, normalized size = 1.01 \[ - \frac {a^{10}}{9 x^{9}} - \frac {15 a^{9} b}{13 x^{\frac {26}{3}}} - \frac {27 a^{8} b^{2}}{5 x^{\frac {25}{3}}} - \frac {15 a^{7} b^{3}}{x^{8}} - \frac {630 a^{6} b^{4}}{23 x^{\frac {23}{3}}} - \frac {378 a^{5} b^{5}}{11 x^{\frac {22}{3}}} - \frac {30 a^{4} b^{6}}{x^{7}} - \frac {18 a^{3} b^{7}}{x^{\frac {20}{3}}} - \frac {135 a^{2} b^{8}}{19 x^{\frac {19}{3}}} - \frac {5 a b^{9}}{3 x^{6}} - \frac {3 b^{10}}{17 x^{\frac {17}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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