Optimal. Leaf size=36 \[ \frac {b (a+b x)^{11}}{132 a^2 x^{11}}-\frac {(a+b x)^{11}}{12 a x^{12}} \]
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Rubi [A] time = 0.00, antiderivative size = 36, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {45, 37} \begin {gather*} \frac {b (a+b x)^{11}}{132 a^2 x^{11}}-\frac {(a+b x)^{11}}{12 a x^{12}} \end {gather*}
Antiderivative was successfully verified.
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Rule 37
Rule 45
Rubi steps
\begin {align*} \int \frac {(a+b x)^{10}}{x^{13}} \, dx &=-\frac {(a+b x)^{11}}{12 a x^{12}}-\frac {b \int \frac {(a+b x)^{10}}{x^{12}} \, dx}{12 a}\\ &=-\frac {(a+b x)^{11}}{12 a x^{12}}+\frac {b (a+b x)^{11}}{132 a^2 x^{11}}\\ \end {align*}
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Mathematica [B] time = 0.00, size = 128, normalized size = 3.56 \begin {gather*} -\frac {a^{10}}{12 x^{12}}-\frac {10 a^9 b}{11 x^{11}}-\frac {9 a^8 b^2}{2 x^{10}}-\frac {40 a^7 b^3}{3 x^9}-\frac {105 a^6 b^4}{4 x^8}-\frac {36 a^5 b^5}{x^7}-\frac {35 a^4 b^6}{x^6}-\frac {24 a^3 b^7}{x^5}-\frac {45 a^2 b^8}{4 x^4}-\frac {10 a b^9}{3 x^3}-\frac {b^{10}}{2 x^2} \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^{13}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 1.34, size = 112, normalized size = 3.11 \begin {gather*} -\frac {66 \, b^{10} x^{10} + 440 \, a b^{9} x^{9} + 1485 \, a^{2} b^{8} x^{8} + 3168 \, a^{3} b^{7} x^{7} + 4620 \, a^{4} b^{6} x^{6} + 4752 \, a^{5} b^{5} x^{5} + 3465 \, a^{6} b^{4} x^{4} + 1760 \, a^{7} b^{3} x^{3} + 594 \, a^{8} b^{2} x^{2} + 120 \, a^{9} b x + 11 \, a^{10}}{132 \, x^{12}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.96, size = 112, normalized size = 3.11 \begin {gather*} -\frac {66 \, b^{10} x^{10} + 440 \, a b^{9} x^{9} + 1485 \, a^{2} b^{8} x^{8} + 3168 \, a^{3} b^{7} x^{7} + 4620 \, a^{4} b^{6} x^{6} + 4752 \, a^{5} b^{5} x^{5} + 3465 \, a^{6} b^{4} x^{4} + 1760 \, a^{7} b^{3} x^{3} + 594 \, a^{8} b^{2} x^{2} + 120 \, a^{9} b x + 11 \, a^{10}}{132 \, x^{12}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.00, size = 113, normalized size = 3.14 \begin {gather*} -\frac {b^{10}}{2 x^{2}}-\frac {10 a \,b^{9}}{3 x^{3}}-\frac {45 a^{2} b^{8}}{4 x^{4}}-\frac {24 a^{3} b^{7}}{x^{5}}-\frac {35 a^{4} b^{6}}{x^{6}}-\frac {36 a^{5} b^{5}}{x^{7}}-\frac {105 a^{6} b^{4}}{4 x^{8}}-\frac {40 a^{7} b^{3}}{3 x^{9}}-\frac {9 a^{8} b^{2}}{2 x^{10}}-\frac {10 a^{9} b}{11 x^{11}}-\frac {a^{10}}{12 x^{12}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.39, size = 112, normalized size = 3.11 \begin {gather*} -\frac {66 \, b^{10} x^{10} + 440 \, a b^{9} x^{9} + 1485 \, a^{2} b^{8} x^{8} + 3168 \, a^{3} b^{7} x^{7} + 4620 \, a^{4} b^{6} x^{6} + 4752 \, a^{5} b^{5} x^{5} + 3465 \, a^{6} b^{4} x^{4} + 1760 \, a^{7} b^{3} x^{3} + 594 \, a^{8} b^{2} x^{2} + 120 \, a^{9} b x + 11 \, a^{10}}{132 \, x^{12}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.10, size = 23, normalized size = 0.64 \begin {gather*} -\frac {\left (11\,a-b\,x\right )\,{\left (a+b\,x\right )}^{11}}{132\,a^2\,x^{12}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.99, size = 121, normalized size = 3.36 \begin {gather*} \frac {- 11 a^{10} - 120 a^{9} b x - 594 a^{8} b^{2} x^{2} - 1760 a^{7} b^{3} x^{3} - 3465 a^{6} b^{4} x^{4} - 4752 a^{5} b^{5} x^{5} - 4620 a^{4} b^{6} x^{6} - 3168 a^{3} b^{7} x^{7} - 1485 a^{2} b^{8} x^{8} - 440 a b^{9} x^{9} - 66 b^{10} x^{10}}{132 x^{12}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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