Optimal. Leaf size=46 \[ \frac {b \left (a+b \sqrt [3]{x}\right )^{11}}{44 a^2 x^{11/3}}-\frac {\left (a+b \sqrt [3]{x}\right )^{11}}{4 a x^4} \]
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Rubi [A] time = 0.01, antiderivative size = 46, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {266, 45, 37} \[ \frac {b \left (a+b \sqrt [3]{x}\right )^{11}}{44 a^2 x^{11/3}}-\frac {\left (a+b \sqrt [3]{x}\right )^{11}}{4 a x^4} \]
Antiderivative was successfully verified.
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Rule 37
Rule 45
Rule 266
Rubi steps
\begin {align*} \int \frac {\left (a+b \sqrt [3]{x}\right )^{10}}{x^5} \, dx &=3 \operatorname {Subst}\left (\int \frac {(a+b x)^{10}}{x^{13}} \, dx,x,\sqrt [3]{x}\right )\\ &=-\frac {\left (a+b \sqrt [3]{x}\right )^{11}}{4 a x^4}-\frac {b \operatorname {Subst}\left (\int \frac {(a+b x)^{10}}{x^{12}} \, dx,x,\sqrt [3]{x}\right )}{4 a}\\ &=-\frac {\left (a+b \sqrt [3]{x}\right )^{11}}{4 a x^4}+\frac {b \left (a+b \sqrt [3]{x}\right )^{11}}{44 a^2 x^{11/3}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 32, normalized size = 0.70 \[ \frac {\left (b \sqrt [3]{x}-11 a\right ) \left (a+b \sqrt [3]{x}\right )^{11}}{44 a^2 x^4} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.75, size = 114, normalized size = 2.48 \[ -\frac {440 \, a b^{9} x^{3} + 4620 \, a^{4} b^{6} x^{2} + 1760 \, a^{7} b^{3} x + 11 \, a^{10} + 297 \, {\left (5 \, a^{2} b^{8} x^{2} + 16 \, a^{5} b^{5} x + 2 \, a^{8} b^{2}\right )} x^{\frac {2}{3}} + 3 \, {\left (22 \, b^{10} x^{3} + 1056 \, a^{3} b^{7} x^{2} + 1155 \, a^{6} b^{4} x + 40 \, a^{9} b\right )} x^{\frac {1}{3}}}{44 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.18, size = 112, normalized size = 2.43 \[ -\frac {66 \, b^{10} x^{\frac {10}{3}} + 440 \, a b^{9} x^{3} + 1485 \, a^{2} b^{8} x^{\frac {8}{3}} + 3168 \, a^{3} b^{7} x^{\frac {7}{3}} + 4620 \, a^{4} b^{6} x^{2} + 4752 \, a^{5} b^{5} x^{\frac {5}{3}} + 3465 \, a^{6} b^{4} x^{\frac {4}{3}} + 1760 \, a^{7} b^{3} x + 594 \, a^{8} b^{2} x^{\frac {2}{3}} + 120 \, a^{9} b x^{\frac {1}{3}} + 11 \, a^{10}}{44 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.01, size = 113, normalized size = 2.46 \[ -\frac {3 b^{10}}{2 x^{\frac {2}{3}}}-\frac {10 a \,b^{9}}{x}-\frac {135 a^{2} b^{8}}{4 x^{\frac {4}{3}}}-\frac {72 a^{3} b^{7}}{x^{\frac {5}{3}}}-\frac {105 a^{4} b^{6}}{x^{2}}-\frac {108 a^{5} b^{5}}{x^{\frac {7}{3}}}-\frac {315 a^{6} b^{4}}{4 x^{\frac {8}{3}}}-\frac {40 a^{7} b^{3}}{x^{3}}-\frac {27 a^{8} b^{2}}{2 x^{\frac {10}{3}}}-\frac {30 a^{9} b}{11 x^{\frac {11}{3}}}-\frac {a^{10}}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.91, size = 112, normalized size = 2.43 \[ -\frac {66 \, b^{10} x^{\frac {10}{3}} + 440 \, a b^{9} x^{3} + 1485 \, a^{2} b^{8} x^{\frac {8}{3}} + 3168 \, a^{3} b^{7} x^{\frac {7}{3}} + 4620 \, a^{4} b^{6} x^{2} + 4752 \, a^{5} b^{5} x^{\frac {5}{3}} + 3465 \, a^{6} b^{4} x^{\frac {4}{3}} + 1760 \, a^{7} b^{3} x + 594 \, a^{8} b^{2} x^{\frac {2}{3}} + 120 \, a^{9} b x^{\frac {1}{3}} + 11 \, a^{10}}{44 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.18, size = 112, normalized size = 2.43 \[ -\frac {\frac {a^{10}}{4}+\frac {3\,b^{10}\,x^{10/3}}{2}+40\,a^7\,b^3\,x+10\,a\,b^9\,x^3+\frac {30\,a^9\,b\,x^{1/3}}{11}+105\,a^4\,b^6\,x^2+\frac {27\,a^8\,b^2\,x^{2/3}}{2}+\frac {315\,a^6\,b^4\,x^{4/3}}{4}+108\,a^5\,b^5\,x^{5/3}+72\,a^3\,b^7\,x^{7/3}+\frac {135\,a^2\,b^8\,x^{8/3}}{4}}{x^4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 3.88, size = 139, normalized size = 3.02 \[ - \frac {a^{10}}{4 x^{4}} - \frac {30 a^{9} b}{11 x^{\frac {11}{3}}} - \frac {27 a^{8} b^{2}}{2 x^{\frac {10}{3}}} - \frac {40 a^{7} b^{3}}{x^{3}} - \frac {315 a^{6} b^{4}}{4 x^{\frac {8}{3}}} - \frac {108 a^{5} b^{5}}{x^{\frac {7}{3}}} - \frac {105 a^{4} b^{6}}{x^{2}} - \frac {72 a^{3} b^{7}}{x^{\frac {5}{3}}} - \frac {135 a^{2} b^{8}}{4 x^{\frac {4}{3}}} - \frac {10 a b^{9}}{x} - \frac {3 b^{10}}{2 x^{\frac {2}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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