Optimal. Leaf size=130 \[ -\frac {a^{10}}{18 x^{18}}-\frac {10 a^9 b}{17 x^{17}}-\frac {45 a^8 b^2}{16 x^{16}}-\frac {8 a^7 b^3}{x^{15}}-\frac {15 a^6 b^4}{x^{14}}-\frac {252 a^5 b^5}{13 x^{13}}-\frac {35 a^4 b^6}{2 x^{12}}-\frac {120 a^3 b^7}{11 x^{11}}-\frac {9 a^2 b^8}{2 x^{10}}-\frac {10 a b^9}{9 x^9}-\frac {b^{10}}{8 x^8} \]
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Rubi [A] time = 0.05, antiderivative size = 130, 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*} -\frac {45 a^8 b^2}{16 x^{16}}-\frac {8 a^7 b^3}{x^{15}}-\frac {15 a^6 b^4}{x^{14}}-\frac {252 a^5 b^5}{13 x^{13}}-\frac {35 a^4 b^6}{2 x^{12}}-\frac {120 a^3 b^7}{11 x^{11}}-\frac {9 a^2 b^8}{2 x^{10}}-\frac {10 a^9 b}{17 x^{17}}-\frac {a^{10}}{18 x^{18}}-\frac {10 a b^9}{9 x^9}-\frac {b^{10}}{8 x^8} \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {(a+b x)^{10}}{x^{19}} \, dx &=\int \left (\frac {a^{10}}{x^{19}}+\frac {10 a^9 b}{x^{18}}+\frac {45 a^8 b^2}{x^{17}}+\frac {120 a^7 b^3}{x^{16}}+\frac {210 a^6 b^4}{x^{15}}+\frac {252 a^5 b^5}{x^{14}}+\frac {210 a^4 b^6}{x^{13}}+\frac {120 a^3 b^7}{x^{12}}+\frac {45 a^2 b^8}{x^{11}}+\frac {10 a b^9}{x^{10}}+\frac {b^{10}}{x^9}\right ) \, dx\\ &=-\frac {a^{10}}{18 x^{18}}-\frac {10 a^9 b}{17 x^{17}}-\frac {45 a^8 b^2}{16 x^{16}}-\frac {8 a^7 b^3}{x^{15}}-\frac {15 a^6 b^4}{x^{14}}-\frac {252 a^5 b^5}{13 x^{13}}-\frac {35 a^4 b^6}{2 x^{12}}-\frac {120 a^3 b^7}{11 x^{11}}-\frac {9 a^2 b^8}{2 x^{10}}-\frac {10 a b^9}{9 x^9}-\frac {b^{10}}{8 x^8}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 130, normalized size = 1.00 \begin {gather*} -\frac {a^{10}}{18 x^{18}}-\frac {10 a^9 b}{17 x^{17}}-\frac {45 a^8 b^2}{16 x^{16}}-\frac {8 a^7 b^3}{x^{15}}-\frac {15 a^6 b^4}{x^{14}}-\frac {252 a^5 b^5}{13 x^{13}}-\frac {35 a^4 b^6}{2 x^{12}}-\frac {120 a^3 b^7}{11 x^{11}}-\frac {9 a^2 b^8}{2 x^{10}}-\frac {10 a b^9}{9 x^9}-\frac {b^{10}}{8 x^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^{19}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.76, size = 112, normalized size = 0.86 \begin {gather*} -\frac {43758 \, b^{10} x^{10} + 388960 \, a b^{9} x^{9} + 1575288 \, a^{2} b^{8} x^{8} + 3818880 \, a^{3} b^{7} x^{7} + 6126120 \, a^{4} b^{6} x^{6} + 6785856 \, a^{5} b^{5} x^{5} + 5250960 \, a^{6} b^{4} x^{4} + 2800512 \, a^{7} b^{3} x^{3} + 984555 \, a^{8} b^{2} x^{2} + 205920 \, a^{9} b x + 19448 \, a^{10}}{350064 \, x^{18}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.98, size = 112, normalized size = 0.86 \begin {gather*} -\frac {43758 \, b^{10} x^{10} + 388960 \, a b^{9} x^{9} + 1575288 \, a^{2} b^{8} x^{8} + 3818880 \, a^{3} b^{7} x^{7} + 6126120 \, a^{4} b^{6} x^{6} + 6785856 \, a^{5} b^{5} x^{5} + 5250960 \, a^{6} b^{4} x^{4} + 2800512 \, a^{7} b^{3} x^{3} + 984555 \, a^{8} b^{2} x^{2} + 205920 \, a^{9} b x + 19448 \, a^{10}}{350064 \, x^{18}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 113, normalized size = 0.87 \begin {gather*} -\frac {b^{10}}{8 x^{8}}-\frac {10 a \,b^{9}}{9 x^{9}}-\frac {9 a^{2} b^{8}}{2 x^{10}}-\frac {120 a^{3} b^{7}}{11 x^{11}}-\frac {35 a^{4} b^{6}}{2 x^{12}}-\frac {252 a^{5} b^{5}}{13 x^{13}}-\frac {15 a^{6} b^{4}}{x^{14}}-\frac {8 a^{7} b^{3}}{x^{15}}-\frac {45 a^{8} b^{2}}{16 x^{16}}-\frac {10 a^{9} b}{17 x^{17}}-\frac {a^{10}}{18 x^{18}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.36, size = 112, normalized size = 0.86 \begin {gather*} -\frac {43758 \, b^{10} x^{10} + 388960 \, a b^{9} x^{9} + 1575288 \, a^{2} b^{8} x^{8} + 3818880 \, a^{3} b^{7} x^{7} + 6126120 \, a^{4} b^{6} x^{6} + 6785856 \, a^{5} b^{5} x^{5} + 5250960 \, a^{6} b^{4} x^{4} + 2800512 \, a^{7} b^{3} x^{3} + 984555 \, a^{8} b^{2} x^{2} + 205920 \, a^{9} b x + 19448 \, a^{10}}{350064 \, x^{18}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.10, size = 112, normalized size = 0.86 \begin {gather*} -\frac {\frac {a^{10}}{18}+\frac {10\,a^9\,b\,x}{17}+\frac {45\,a^8\,b^2\,x^2}{16}+8\,a^7\,b^3\,x^3+15\,a^6\,b^4\,x^4+\frac {252\,a^5\,b^5\,x^5}{13}+\frac {35\,a^4\,b^6\,x^6}{2}+\frac {120\,a^3\,b^7\,x^7}{11}+\frac {9\,a^2\,b^8\,x^8}{2}+\frac {10\,a\,b^9\,x^9}{9}+\frac {b^{10}\,x^{10}}{8}}{x^{18}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.35, size = 121, normalized size = 0.93 \begin {gather*} \frac {- 19448 a^{10} - 205920 a^{9} b x - 984555 a^{8} b^{2} x^{2} - 2800512 a^{7} b^{3} x^{3} - 5250960 a^{6} b^{4} x^{4} - 6785856 a^{5} b^{5} x^{5} - 6126120 a^{4} b^{6} x^{6} - 3818880 a^{3} b^{7} x^{7} - 1575288 a^{2} b^{8} x^{8} - 388960 a b^{9} x^{9} - 43758 b^{10} x^{10}}{350064 x^{18}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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