Optimal. Leaf size=69 \[ -\frac {a^5}{18 x^{18}}-\frac {5 a^4 b}{16 x^{16}}-\frac {5 a^3 b^2}{7 x^{14}}-\frac {5 a^2 b^3}{6 x^{12}}-\frac {a b^4}{2 x^{10}}-\frac {b^5}{8 x^8} \]
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Rubi [A] time = 0.03, antiderivative size = 69, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {266, 43} \begin {gather*} -\frac {5 a^3 b^2}{7 x^{14}}-\frac {5 a^2 b^3}{6 x^{12}}-\frac {5 a^4 b}{16 x^{16}}-\frac {a^5}{18 x^{18}}-\frac {a b^4}{2 x^{10}}-\frac {b^5}{8 x^8} \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rule 266
Rubi steps
\begin {align*} \int \frac {\left (a+b x^2\right )^5}{x^{19}} \, dx &=\frac {1}{2} \operatorname {Subst}\left (\int \frac {(a+b x)^5}{x^{10}} \, dx,x,x^2\right )\\ &=\frac {1}{2} \operatorname {Subst}\left (\int \left (\frac {a^5}{x^{10}}+\frac {5 a^4 b}{x^9}+\frac {10 a^3 b^2}{x^8}+\frac {10 a^2 b^3}{x^7}+\frac {5 a b^4}{x^6}+\frac {b^5}{x^5}\right ) \, dx,x,x^2\right )\\ &=-\frac {a^5}{18 x^{18}}-\frac {5 a^4 b}{16 x^{16}}-\frac {5 a^3 b^2}{7 x^{14}}-\frac {5 a^2 b^3}{6 x^{12}}-\frac {a b^4}{2 x^{10}}-\frac {b^5}{8 x^8}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 69, normalized size = 1.00 \begin {gather*} -\frac {a^5}{18 x^{18}}-\frac {5 a^4 b}{16 x^{16}}-\frac {5 a^3 b^2}{7 x^{14}}-\frac {5 a^2 b^3}{6 x^{12}}-\frac {a b^4}{2 x^{10}}-\frac {b^5}{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 {\left (a+b x^2\right )^5}{x^{19}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.12, size = 59, normalized size = 0.86 \begin {gather*} -\frac {126 \, b^{5} x^{10} + 504 \, a b^{4} x^{8} + 840 \, a^{2} b^{3} x^{6} + 720 \, a^{3} b^{2} x^{4} + 315 \, a^{4} b x^{2} + 56 \, a^{5}}{1008 \, x^{18}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.94, size = 59, normalized size = 0.86 \begin {gather*} -\frac {126 \, b^{5} x^{10} + 504 \, a b^{4} x^{8} + 840 \, a^{2} b^{3} x^{6} + 720 \, a^{3} b^{2} x^{4} + 315 \, a^{4} b x^{2} + 56 \, a^{5}}{1008 \, x^{18}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 58, normalized size = 0.84 \begin {gather*} -\frac {b^{5}}{8 x^{8}}-\frac {a \,b^{4}}{2 x^{10}}-\frac {5 a^{2} b^{3}}{6 x^{12}}-\frac {5 a^{3} b^{2}}{7 x^{14}}-\frac {5 a^{4} b}{16 x^{16}}-\frac {a^{5}}{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 = 59, normalized size = 0.86 \begin {gather*} -\frac {126 \, b^{5} x^{10} + 504 \, a b^{4} x^{8} + 840 \, a^{2} b^{3} x^{6} + 720 \, a^{3} b^{2} x^{4} + 315 \, a^{4} b x^{2} + 56 \, a^{5}}{1008 \, x^{18}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 59, normalized size = 0.86 \begin {gather*} -\frac {\frac {a^5}{18}+\frac {5\,a^4\,b\,x^2}{16}+\frac {5\,a^3\,b^2\,x^4}{7}+\frac {5\,a^2\,b^3\,x^6}{6}+\frac {a\,b^4\,x^8}{2}+\frac {b^5\,x^{10}}{8}}{x^{18}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.59, size = 63, normalized size = 0.91 \begin {gather*} \frac {- 56 a^{5} - 315 a^{4} b x^{2} - 720 a^{3} b^{2} x^{4} - 840 a^{2} b^{3} x^{6} - 504 a b^{4} x^{8} - 126 b^{5} x^{10}}{1008 x^{18}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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