Optimal. Leaf size=136 \[ a^{10} \log (x)+30 a^9 b \sqrt [3]{x}+\frac {135}{2} a^8 b^2 x^{2/3}+120 a^7 b^3 x+\frac {315}{2} a^6 b^4 x^{4/3}+\frac {756}{5} a^5 b^5 x^{5/3}+105 a^4 b^6 x^2+\frac {360}{7} a^3 b^7 x^{7/3}+\frac {135}{8} a^2 b^8 x^{8/3}+\frac {10}{3} a b^9 x^3+\frac {3}{10} b^{10} x^{10/3} \]
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Rubi [A] time = 0.07, antiderivative size = 136, 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} \[ \frac {135}{2} a^8 b^2 x^{2/3}+\frac {315}{2} a^6 b^4 x^{4/3}+\frac {756}{5} a^5 b^5 x^{5/3}+105 a^4 b^6 x^2+\frac {360}{7} a^3 b^7 x^{7/3}+\frac {135}{8} a^2 b^8 x^{8/3}+120 a^7 b^3 x+30 a^9 b \sqrt [3]{x}+a^{10} \log (x)+\frac {10}{3} a b^9 x^3+\frac {3}{10} b^{10} x^{10/3} \]
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} \, dx &=3 \operatorname {Subst}\left (\int \frac {(a+b x)^{10}}{x} \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname {Subst}\left (\int \left (10 a^9 b+\frac {a^{10}}{x}+45 a^8 b^2 x+120 a^7 b^3 x^2+210 a^6 b^4 x^3+252 a^5 b^5 x^4+210 a^4 b^6 x^5+120 a^3 b^7 x^6+45 a^2 b^8 x^7+10 a b^9 x^8+b^{10} x^9\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=30 a^9 b \sqrt [3]{x}+\frac {135}{2} a^8 b^2 x^{2/3}+120 a^7 b^3 x+\frac {315}{2} a^6 b^4 x^{4/3}+\frac {756}{5} a^5 b^5 x^{5/3}+105 a^4 b^6 x^2+\frac {360}{7} a^3 b^7 x^{7/3}+\frac {135}{8} a^2 b^8 x^{8/3}+\frac {10}{3} a b^9 x^3+\frac {3}{10} b^{10} x^{10/3}+a^{10} \log (x)\\ \end {align*}
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Mathematica [A] time = 0.08, size = 136, normalized size = 1.00 \[ a^{10} \log (x)+30 a^9 b \sqrt [3]{x}+\frac {135}{2} a^8 b^2 x^{2/3}+120 a^7 b^3 x+\frac {315}{2} a^6 b^4 x^{4/3}+\frac {756}{5} a^5 b^5 x^{5/3}+105 a^4 b^6 x^2+\frac {360}{7} a^3 b^7 x^{7/3}+\frac {135}{8} a^2 b^8 x^{8/3}+\frac {10}{3} a b^9 x^3+\frac {3}{10} b^{10} x^{10/3} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.93, size = 113, normalized size = 0.83 \[ \frac {10}{3} \, a b^{9} x^{3} + 105 \, a^{4} b^{6} x^{2} + 120 \, a^{7} b^{3} x + 3 \, a^{10} \log \left (x^{\frac {1}{3}}\right ) + \frac {27}{40} \, {\left (25 \, a^{2} b^{8} x^{2} + 224 \, a^{5} b^{5} x + 100 \, a^{8} b^{2}\right )} x^{\frac {2}{3}} + \frac {3}{70} \, {\left (7 \, b^{10} x^{3} + 1200 \, a^{3} b^{7} x^{2} + 3675 \, a^{6} b^{4} x + 700 \, a^{9} b\right )} x^{\frac {1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 109, normalized size = 0.80 \[ \frac {3}{10} \, b^{10} x^{\frac {10}{3}} + \frac {10}{3} \, a b^{9} x^{3} + \frac {135}{8} \, a^{2} b^{8} x^{\frac {8}{3}} + \frac {360}{7} \, a^{3} b^{7} x^{\frac {7}{3}} + 105 \, a^{4} b^{6} x^{2} + \frac {756}{5} \, a^{5} b^{5} x^{\frac {5}{3}} + \frac {315}{2} \, a^{6} b^{4} x^{\frac {4}{3}} + 120 \, a^{7} b^{3} x + a^{10} \log \left ({\left | x \right |}\right ) + \frac {135}{2} \, a^{8} b^{2} x^{\frac {2}{3}} + 30 \, a^{9} b x^{\frac {1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 109, normalized size = 0.80 \[ \frac {3 b^{10} x^{\frac {10}{3}}}{10}+\frac {10 a \,b^{9} x^{3}}{3}+\frac {135 a^{2} b^{8} x^{\frac {8}{3}}}{8}+\frac {360 a^{3} b^{7} x^{\frac {7}{3}}}{7}+105 a^{4} b^{6} x^{2}+\frac {756 a^{5} b^{5} x^{\frac {5}{3}}}{5}+\frac {315 a^{6} b^{4} x^{\frac {4}{3}}}{2}+a^{10} \ln \relax (x )+120 a^{7} b^{3} x +\frac {135 a^{8} b^{2} x^{\frac {2}{3}}}{2}+30 a^{9} b \,x^{\frac {1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.90, size = 108, normalized size = 0.79 \[ \frac {3}{10} \, b^{10} x^{\frac {10}{3}} + \frac {10}{3} \, a b^{9} x^{3} + \frac {135}{8} \, a^{2} b^{8} x^{\frac {8}{3}} + \frac {360}{7} \, a^{3} b^{7} x^{\frac {7}{3}} + 105 \, a^{4} b^{6} x^{2} + \frac {756}{5} \, a^{5} b^{5} x^{\frac {5}{3}} + \frac {315}{2} \, a^{6} b^{4} x^{\frac {4}{3}} + 120 \, a^{7} b^{3} x + a^{10} \log \relax (x) + \frac {135}{2} \, a^{8} b^{2} x^{\frac {2}{3}} + 30 \, a^{9} b x^{\frac {1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 111, normalized size = 0.82 \[ 3\,a^{10}\,\ln \left (x^{1/3}\right )+\frac {3\,b^{10}\,x^{10/3}}{10}+120\,a^7\,b^3\,x+\frac {10\,a\,b^9\,x^3}{3}+30\,a^9\,b\,x^{1/3}+105\,a^4\,b^6\,x^2+\frac {135\,a^8\,b^2\,x^{2/3}}{2}+\frac {315\,a^6\,b^4\,x^{4/3}}{2}+\frac {756\,a^5\,b^5\,x^{5/3}}{5}+\frac {360\,a^3\,b^7\,x^{7/3}}{7}+\frac {135\,a^2\,b^8\,x^{8/3}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 66.36, size = 139, normalized size = 1.02 \[ a^{10} \log {\relax (x )} + 30 a^{9} b \sqrt [3]{x} + \frac {135 a^{8} b^{2} x^{\frac {2}{3}}}{2} + 120 a^{7} b^{3} x + \frac {315 a^{6} b^{4} x^{\frac {4}{3}}}{2} + \frac {756 a^{5} b^{5} x^{\frac {5}{3}}}{5} + 105 a^{4} b^{6} x^{2} + \frac {360 a^{3} b^{7} x^{\frac {7}{3}}}{7} + \frac {135 a^{2} b^{8} x^{\frac {8}{3}}}{8} + \frac {10 a b^{9} x^{3}}{3} + \frac {3 b^{10} x^{\frac {10}{3}}}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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