Optimal. Leaf size=119 \[ -\frac {a^{10}}{2 x^2}-\frac {10 a^9 b}{x}+45 a^8 b^2 \log (x)+120 a^7 b^3 x+105 a^6 b^4 x^2+84 a^5 b^5 x^3+\frac {105}{2} a^4 b^6 x^4+24 a^3 b^7 x^5+\frac {15}{2} a^2 b^8 x^6+\frac {10}{7} a b^9 x^7+\frac {b^{10} x^8}{8} \]
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Rubi [A] time = 0.05, antiderivative size = 119, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {43} \begin {gather*} 105 a^6 b^4 x^2+84 a^5 b^5 x^3+\frac {105}{2} a^4 b^6 x^4+24 a^3 b^7 x^5+\frac {15}{2} a^2 b^8 x^6+120 a^7 b^3 x+45 a^8 b^2 \log (x)-\frac {10 a^9 b}{x}-\frac {a^{10}}{2 x^2}+\frac {10}{7} a b^9 x^7+\frac {b^{10} x^8}{8} \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {(a+b x)^{10}}{x^3} \, dx &=\int \left (120 a^7 b^3+\frac {a^{10}}{x^3}+\frac {10 a^9 b}{x^2}+\frac {45 a^8 b^2}{x}+210 a^6 b^4 x+252 a^5 b^5 x^2+210 a^4 b^6 x^3+120 a^3 b^7 x^4+45 a^2 b^8 x^5+10 a b^9 x^6+b^{10} x^7\right ) \, dx\\ &=-\frac {a^{10}}{2 x^2}-\frac {10 a^9 b}{x}+120 a^7 b^3 x+105 a^6 b^4 x^2+84 a^5 b^5 x^3+\frac {105}{2} a^4 b^6 x^4+24 a^3 b^7 x^5+\frac {15}{2} a^2 b^8 x^6+\frac {10}{7} a b^9 x^7+\frac {b^{10} x^8}{8}+45 a^8 b^2 \log (x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 119, normalized size = 1.00 \begin {gather*} -\frac {a^{10}}{2 x^2}-\frac {10 a^9 b}{x}+45 a^8 b^2 \log (x)+120 a^7 b^3 x+105 a^6 b^4 x^2+84 a^5 b^5 x^3+\frac {105}{2} a^4 b^6 x^4+24 a^3 b^7 x^5+\frac {15}{2} a^2 b^8 x^6+\frac {10}{7} a b^9 x^7+\frac {b^{10} x^8}{8} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(a+b x)^{10}}{x^3} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.41, size = 114, normalized size = 0.96 \begin {gather*} \frac {7 \, b^{10} x^{10} + 80 \, a b^{9} x^{9} + 420 \, a^{2} b^{8} x^{8} + 1344 \, a^{3} b^{7} x^{7} + 2940 \, a^{4} b^{6} x^{6} + 4704 \, a^{5} b^{5} x^{5} + 5880 \, a^{6} b^{4} x^{4} + 6720 \, a^{7} b^{3} x^{3} + 2520 \, a^{8} b^{2} x^{2} \log \relax (x) - 560 \, a^{9} b x - 28 \, a^{10}}{56 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.93, size = 109, normalized size = 0.92 \begin {gather*} \frac {1}{8} \, b^{10} x^{8} + \frac {10}{7} \, a b^{9} x^{7} + \frac {15}{2} \, a^{2} b^{8} x^{6} + 24 \, a^{3} b^{7} x^{5} + \frac {105}{2} \, a^{4} b^{6} x^{4} + 84 \, a^{5} b^{5} x^{3} + 105 \, a^{6} b^{4} x^{2} + 120 \, a^{7} b^{3} x + 45 \, a^{8} b^{2} \log \left ({\left | x \right |}\right ) - \frac {20 \, a^{9} b x + a^{10}}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 110, normalized size = 0.92 \begin {gather*} \frac {b^{10} x^{8}}{8}+\frac {10 a \,b^{9} x^{7}}{7}+\frac {15 a^{2} b^{8} x^{6}}{2}+24 a^{3} b^{7} x^{5}+\frac {105 a^{4} b^{6} x^{4}}{2}+84 a^{5} b^{5} x^{3}+105 a^{6} b^{4} x^{2}+45 a^{8} b^{2} \ln \relax (x )+120 a^{7} b^{3} x -\frac {10 a^{9} b}{x}-\frac {a^{10}}{2 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.44, size = 108, normalized size = 0.91 \begin {gather*} \frac {1}{8} \, b^{10} x^{8} + \frac {10}{7} \, a b^{9} x^{7} + \frac {15}{2} \, a^{2} b^{8} x^{6} + 24 \, a^{3} b^{7} x^{5} + \frac {105}{2} \, a^{4} b^{6} x^{4} + 84 \, a^{5} b^{5} x^{3} + 105 \, a^{6} b^{4} x^{2} + 120 \, a^{7} b^{3} x + 45 \, a^{8} b^{2} \log \relax (x) - \frac {20 \, a^{9} b x + a^{10}}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 110, normalized size = 0.92 \begin {gather*} \frac {b^{10}\,x^8}{8}-\frac {\frac {a^{10}}{2}+10\,b\,x\,a^9}{x^2}+120\,a^7\,b^3\,x+\frac {10\,a\,b^9\,x^7}{7}+105\,a^6\,b^4\,x^2+84\,a^5\,b^5\,x^3+\frac {105\,a^4\,b^6\,x^4}{2}+24\,a^3\,b^7\,x^5+\frac {15\,a^2\,b^8\,x^6}{2}+45\,a^8\,b^2\,\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.31, size = 122, normalized size = 1.03 \begin {gather*} 45 a^{8} b^{2} \log {\relax (x )} + 120 a^{7} b^{3} x + 105 a^{6} b^{4} x^{2} + 84 a^{5} b^{5} x^{3} + \frac {105 a^{4} b^{6} x^{4}}{2} + 24 a^{3} b^{7} x^{5} + \frac {15 a^{2} b^{8} x^{6}}{2} + \frac {10 a b^{9} x^{7}}{7} + \frac {b^{10} x^{8}}{8} + \frac {- a^{10} - 20 a^{9} b x}{2 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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