Optimal. Leaf size=62 \[ -\frac {b^2 \left (a+b x^2\right )^6}{336 a^3 x^{12}}+\frac {b \left (a+b x^2\right )^6}{56 a^2 x^{14}}-\frac {\left (a+b x^2\right )^6}{16 a x^{16}} \]
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Rubi [A] time = 0.03, antiderivative size = 62, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.231, Rules used = {266, 45, 37} \begin {gather*} -\frac {b^2 \left (a+b x^2\right )^6}{336 a^3 x^{12}}+\frac {b \left (a+b x^2\right )^6}{56 a^2 x^{14}}-\frac {\left (a+b x^2\right )^6}{16 a x^{16}} \end {gather*}
Antiderivative was successfully verified.
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Rule 37
Rule 45
Rule 266
Rubi steps
\begin {align*} \int \frac {\left (a+b x^2\right )^5}{x^{17}} \, dx &=\frac {1}{2} \operatorname {Subst}\left (\int \frac {(a+b x)^5}{x^9} \, dx,x,x^2\right )\\ &=-\frac {\left (a+b x^2\right )^6}{16 a x^{16}}-\frac {b \operatorname {Subst}\left (\int \frac {(a+b x)^5}{x^8} \, dx,x,x^2\right )}{8 a}\\ &=-\frac {\left (a+b x^2\right )^6}{16 a x^{16}}+\frac {b \left (a+b x^2\right )^6}{56 a^2 x^{14}}+\frac {b^2 \operatorname {Subst}\left (\int \frac {(a+b x)^5}{x^7} \, dx,x,x^2\right )}{56 a^2}\\ &=-\frac {\left (a+b x^2\right )^6}{16 a x^{16}}+\frac {b \left (a+b x^2\right )^6}{56 a^2 x^{14}}-\frac {b^2 \left (a+b x^2\right )^6}{336 a^3 x^{12}}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 67, normalized size = 1.08 \begin {gather*} -\frac {a^5}{16 x^{16}}-\frac {5 a^4 b}{14 x^{14}}-\frac {5 a^3 b^2}{6 x^{12}}-\frac {a^2 b^3}{x^{10}}-\frac {5 a b^4}{8 x^8}-\frac {b^5}{6 x^6} \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^{17}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.01, size = 59, normalized size = 0.95 \begin {gather*} -\frac {56 \, b^{5} x^{10} + 210 \, a b^{4} x^{8} + 336 \, a^{2} b^{3} x^{6} + 280 \, a^{3} b^{2} x^{4} + 120 \, a^{4} b x^{2} + 21 \, a^{5}}{336 \, x^{16}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.98, size = 59, normalized size = 0.95 \begin {gather*} -\frac {56 \, b^{5} x^{10} + 210 \, a b^{4} x^{8} + 336 \, a^{2} b^{3} x^{6} + 280 \, a^{3} b^{2} x^{4} + 120 \, a^{4} b x^{2} + 21 \, a^{5}}{336 \, x^{16}} \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 = 0.94 \begin {gather*} -\frac {b^{5}}{6 x^{6}}-\frac {5 a \,b^{4}}{8 x^{8}}-\frac {a^{2} b^{3}}{x^{10}}-\frac {5 a^{3} b^{2}}{6 x^{12}}-\frac {5 a^{4} b}{14 x^{14}}-\frac {a^{5}}{16 x^{16}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.38, size = 59, normalized size = 0.95 \begin {gather*} -\frac {56 \, b^{5} x^{10} + 210 \, a b^{4} x^{8} + 336 \, a^{2} b^{3} x^{6} + 280 \, a^{3} b^{2} x^{4} + 120 \, a^{4} b x^{2} + 21 \, a^{5}}{336 \, x^{16}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 58, normalized size = 0.94 \begin {gather*} -\frac {\frac {a^5}{16}+\frac {5\,a^4\,b\,x^2}{14}+\frac {5\,a^3\,b^2\,x^4}{6}+a^2\,b^3\,x^6+\frac {5\,a\,b^4\,x^8}{8}+\frac {b^5\,x^{10}}{6}}{x^{16}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.55, size = 63, normalized size = 1.02 \begin {gather*} \frac {- 21 a^{5} - 120 a^{4} b x^{2} - 280 a^{3} b^{2} x^{4} - 336 a^{2} b^{3} x^{6} - 210 a b^{4} x^{8} - 56 b^{5} x^{10}}{336 x^{16}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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