Optimal. Leaf size=19 \[ -\frac {\left (a+b x^2\right )^6}{12 a x^{12}} \]
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Rubi [A] time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {264} \begin {gather*} -\frac {\left (a+b x^2\right )^6}{12 a x^{12}} \end {gather*}
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin {align*} \int \frac {\left (a+b x^2\right )^5}{x^{13}} \, dx &=-\frac {\left (a+b x^2\right )^6}{12 a x^{12}}\\ \end {align*}
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Mathematica [B] time = 0.00, size = 69, normalized size = 3.63 \begin {gather*} -\frac {a^5}{12 x^{12}}-\frac {a^4 b}{2 x^{10}}-\frac {5 a^3 b^2}{4 x^8}-\frac {5 a^2 b^3}{3 x^6}-\frac {5 a b^4}{4 x^4}-\frac {b^5}{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 {\left (a+b x^2\right )^5}{x^{13}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 0.60, size = 57, normalized size = 3.00 \begin {gather*} -\frac {6 \, b^{5} x^{10} + 15 \, a b^{4} x^{8} + 20 \, a^{2} b^{3} x^{6} + 15 \, a^{3} b^{2} x^{4} + 6 \, a^{4} b x^{2} + a^{5}}{12 \, x^{12}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.07, size = 57, normalized size = 3.00 \begin {gather*} -\frac {6 \, b^{5} x^{10} + 15 \, a b^{4} x^{8} + 20 \, a^{2} b^{3} x^{6} + 15 \, a^{3} b^{2} x^{4} + 6 \, a^{4} b x^{2} + a^{5}}{12 \, x^{12}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.01, size = 58, normalized size = 3.05 \begin {gather*} -\frac {b^{5}}{2 x^{2}}-\frac {5 a \,b^{4}}{4 x^{4}}-\frac {5 a^{2} b^{3}}{3 x^{6}}-\frac {5 a^{3} b^{2}}{4 x^{8}}-\frac {a^{4} b}{2 x^{10}}-\frac {a^{5}}{12 x^{12}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.37, size = 57, normalized size = 3.00 \begin {gather*} -\frac {6 \, b^{5} x^{10} + 15 \, a b^{4} x^{8} + 20 \, a^{2} b^{3} x^{6} + 15 \, a^{3} b^{2} x^{4} + 6 \, a^{4} b x^{2} + a^{5}}{12 \, x^{12}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.75, size = 59, normalized size = 3.11 \begin {gather*} -\frac {\frac {a^5}{12}+\frac {a^4\,b\,x^2}{2}+\frac {5\,a^3\,b^2\,x^4}{4}+\frac {5\,a^2\,b^3\,x^6}{3}+\frac {5\,a\,b^4\,x^8}{4}+\frac {b^5\,x^{10}}{2}}{x^{12}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.47, size = 61, normalized size = 3.21 \begin {gather*} \frac {- a^{5} - 6 a^{4} b x^{2} - 15 a^{3} b^{2} x^{4} - 20 a^{2} b^{3} x^{6} - 15 a b^{4} x^{8} - 6 b^{5} x^{10}}{12 x^{12}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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