Optimal. Leaf size=125 \[ -\frac {a^{10}}{x}-\frac {15 a^9 b}{x^{2/3}}-\frac {135 a^8 b^2}{\sqrt [3]{x}}+120 a^7 b^3 \log (x)+630 a^6 b^4 \sqrt [3]{x}+378 a^5 b^5 x^{2/3}+210 a^4 b^6 x+90 a^3 b^7 x^{4/3}+27 a^2 b^8 x^{5/3}+5 a b^9 x^2+\frac {3}{7} b^{10} x^{7/3} \]
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Rubi [A] time = 0.07, antiderivative size = 125, 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} \[ 378 a^5 b^5 x^{2/3}+90 a^3 b^7 x^{4/3}+27 a^2 b^8 x^{5/3}-\frac {135 a^8 b^2}{\sqrt [3]{x}}+630 a^6 b^4 \sqrt [3]{x}+210 a^4 b^6 x+120 a^7 b^3 \log (x)-\frac {15 a^9 b}{x^{2/3}}-\frac {a^{10}}{x}+5 a b^9 x^2+\frac {3}{7} b^{10} x^{7/3} \]
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^2} \, dx &=3 \operatorname {Subst}\left (\int \frac {(a+b x)^{10}}{x^4} \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname {Subst}\left (\int \left (210 a^6 b^4+\frac {a^{10}}{x^4}+\frac {10 a^9 b}{x^3}+\frac {45 a^8 b^2}{x^2}+\frac {120 a^7 b^3}{x}+252 a^5 b^5 x+210 a^4 b^6 x^2+120 a^3 b^7 x^3+45 a^2 b^8 x^4+10 a b^9 x^5+b^{10} x^6\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=-\frac {a^{10}}{x}-\frac {15 a^9 b}{x^{2/3}}-\frac {135 a^8 b^2}{\sqrt [3]{x}}+630 a^6 b^4 \sqrt [3]{x}+378 a^5 b^5 x^{2/3}+210 a^4 b^6 x+90 a^3 b^7 x^{4/3}+27 a^2 b^8 x^{5/3}+5 a b^9 x^2+\frac {3}{7} b^{10} x^{7/3}+120 a^7 b^3 \log (x)\\ \end {align*}
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Mathematica [A] time = 0.08, size = 125, normalized size = 1.00 \[ -\frac {a^{10}}{x}-\frac {15 a^9 b}{x^{2/3}}-\frac {135 a^8 b^2}{\sqrt [3]{x}}+120 a^7 b^3 \log (x)+630 a^6 b^4 \sqrt [3]{x}+378 a^5 b^5 x^{2/3}+210 a^4 b^6 x+90 a^3 b^7 x^{4/3}+27 a^2 b^8 x^{5/3}+5 a b^9 x^2+\frac {3}{7} b^{10} x^{7/3} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.82, size = 116, normalized size = 0.93 \[ \frac {35 \, a b^{9} x^{3} + 1470 \, a^{4} b^{6} x^{2} + 2520 \, a^{7} b^{3} x \log \left (x^{\frac {1}{3}}\right ) - 7 \, a^{10} + 189 \, {\left (a^{2} b^{8} x^{2} + 14 \, a^{5} b^{5} x - 5 \, a^{8} b^{2}\right )} x^{\frac {2}{3}} + 3 \, {\left (b^{10} x^{3} + 210 \, a^{3} b^{7} x^{2} + 1470 \, a^{6} b^{4} x - 35 \, a^{9} b\right )} x^{\frac {1}{3}}}{7 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 111, normalized size = 0.89 \[ \frac {3}{7} \, b^{10} x^{\frac {7}{3}} + 5 \, a b^{9} x^{2} + 27 \, a^{2} b^{8} x^{\frac {5}{3}} + 90 \, a^{3} b^{7} x^{\frac {4}{3}} + 210 \, a^{4} b^{6} x + 120 \, a^{7} b^{3} \log \left ({\left | x \right |}\right ) + 378 \, a^{5} b^{5} x^{\frac {2}{3}} + 630 \, a^{6} b^{4} x^{\frac {1}{3}} - \frac {135 \, a^{8} b^{2} x^{\frac {2}{3}} + 15 \, a^{9} b x^{\frac {1}{3}} + a^{10}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 110, normalized size = 0.88 \[ \frac {3 b^{10} x^{\frac {7}{3}}}{7}+5 a \,b^{9} x^{2}+27 a^{2} b^{8} x^{\frac {5}{3}}+90 a^{3} b^{7} x^{\frac {4}{3}}+120 a^{7} b^{3} \ln \relax (x )+210 a^{4} b^{6} x +378 a^{5} b^{5} x^{\frac {2}{3}}+630 a^{6} b^{4} x^{\frac {1}{3}}-\frac {135 a^{8} b^{2}}{x^{\frac {1}{3}}}-\frac {15 a^{9} b}{x^{\frac {2}{3}}}-\frac {a^{10}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.93, size = 110, normalized size = 0.88 \[ \frac {3}{7} \, b^{10} x^{\frac {7}{3}} + 5 \, a b^{9} x^{2} + 27 \, a^{2} b^{8} x^{\frac {5}{3}} + 90 \, a^{3} b^{7} x^{\frac {4}{3}} + 210 \, a^{4} b^{6} x + 120 \, a^{7} b^{3} \log \relax (x) + 378 \, a^{5} b^{5} x^{\frac {2}{3}} + 630 \, a^{6} b^{4} x^{\frac {1}{3}} - \frac {135 \, a^{8} b^{2} x^{\frac {2}{3}} + 15 \, a^{9} b x^{\frac {1}{3}} + a^{10}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 112, normalized size = 0.90 \[ \frac {3\,b^{10}\,x^{7/3}}{7}-\frac {a^{10}+15\,a^9\,b\,x^{1/3}+135\,a^8\,b^2\,x^{2/3}}{x}+360\,a^7\,b^3\,\ln \left (x^{1/3}\right )+210\,a^4\,b^6\,x+5\,a\,b^9\,x^2+630\,a^6\,b^4\,x^{1/3}+378\,a^5\,b^5\,x^{2/3}+90\,a^3\,b^7\,x^{4/3}+27\,a^2\,b^8\,x^{5/3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 15.71, size = 131, normalized size = 1.05 \[ - \frac {a^{10}}{x} - \frac {15 a^{9} b}{x^{\frac {2}{3}}} - \frac {135 a^{8} b^{2}}{\sqrt [3]{x}} + 360 a^{7} b^{3} \log {\left (\sqrt [3]{x} \right )} + 630 a^{6} b^{4} \sqrt [3]{x} + 378 a^{5} b^{5} x^{\frac {2}{3}} + 210 a^{4} b^{6} x + 90 a^{3} b^{7} x^{\frac {4}{3}} + 27 a^{2} b^{8} x^{\frac {5}{3}} + 5 a b^{9} x^{2} + \frac {3 b^{10} x^{\frac {7}{3}}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
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