Optimal. Leaf size=43 \[ -\frac {b^3}{9 x^9}-\frac {3 b^2 c}{7 x^7}-\frac {3 b c^2}{5 x^5}-\frac {c^3}{3 x^3} \]
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Rubi [A] time = 0.02, antiderivative size = 43, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {1584, 270} \begin {gather*} -\frac {3 b^2 c}{7 x^7}-\frac {b^3}{9 x^9}-\frac {3 b c^2}{5 x^5}-\frac {c^3}{3 x^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 270
Rule 1584
Rubi steps
\begin {align*} \int \frac {\left (b x^2+c x^4\right )^3}{x^{16}} \, dx &=\int \frac {\left (b+c x^2\right )^3}{x^{10}} \, dx\\ &=\int \left (\frac {b^3}{x^{10}}+\frac {3 b^2 c}{x^8}+\frac {3 b c^2}{x^6}+\frac {c^3}{x^4}\right ) \, dx\\ &=-\frac {b^3}{9 x^9}-\frac {3 b^2 c}{7 x^7}-\frac {3 b c^2}{5 x^5}-\frac {c^3}{3 x^3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 43, normalized size = 1.00 \begin {gather*} -\frac {b^3}{9 x^9}-\frac {3 b^2 c}{7 x^7}-\frac {3 b c^2}{5 x^5}-\frac {c^3}{3 x^3} \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 (b x^2+c x^4\right )^3}{x^{16}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.61, size = 37, normalized size = 0.86 \begin {gather*} -\frac {105 \, c^{3} x^{6} + 189 \, b c^{2} x^{4} + 135 \, b^{2} c x^{2} + 35 \, b^{3}}{315 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 37, normalized size = 0.86 \begin {gather*} -\frac {105 \, c^{3} x^{6} + 189 \, b c^{2} x^{4} + 135 \, b^{2} c x^{2} + 35 \, b^{3}}{315 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 36, normalized size = 0.84 \begin {gather*} -\frac {c^{3}}{3 x^{3}}-\frac {3 b \,c^{2}}{5 x^{5}}-\frac {3 b^{2} c}{7 x^{7}}-\frac {b^{3}}{9 x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.33, size = 37, normalized size = 0.86 \begin {gather*} -\frac {105 \, c^{3} x^{6} + 189 \, b c^{2} x^{4} + 135 \, b^{2} c x^{2} + 35 \, b^{3}}{315 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 37, normalized size = 0.86 \begin {gather*} -\frac {\frac {b^3}{9}+\frac {3\,b^2\,c\,x^2}{7}+\frac {3\,b\,c^2\,x^4}{5}+\frac {c^3\,x^6}{3}}{x^9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.30, size = 39, normalized size = 0.91 \begin {gather*} \frac {- 35 b^{3} - 135 b^{2} c x^{2} - 189 b c^{2} x^{4} - 105 c^{3} x^{6}}{315 x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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