Optimal. Leaf size=40 \[ \frac{c \left (b+c x^2\right )^4}{40 b^2 x^8}-\frac{\left (b+c x^2\right )^4}{10 b x^{10}} \]
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Rubi [A] time = 0.0232954, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.235, Rules used = {1584, 266, 45, 37} \[ \frac{c \left (b+c x^2\right )^4}{40 b^2 x^8}-\frac{\left (b+c x^2\right )^4}{10 b x^{10}} \]
Antiderivative was successfully verified.
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Rule 1584
Rule 266
Rule 45
Rule 37
Rubi steps
\begin{align*} \int \frac{\left (b x^2+c x^4\right )^3}{x^{17}} \, dx &=\int \frac{\left (b+c x^2\right )^3}{x^{11}} \, dx\\ &=\frac{1}{2} \operatorname{Subst}\left (\int \frac{(b+c x)^3}{x^6} \, dx,x,x^2\right )\\ &=-\frac{\left (b+c x^2\right )^4}{10 b x^{10}}-\frac{c \operatorname{Subst}\left (\int \frac{(b+c x)^3}{x^5} \, dx,x,x^2\right )}{10 b}\\ &=-\frac{\left (b+c x^2\right )^4}{10 b x^{10}}+\frac{c \left (b+c x^2\right )^4}{40 b^2 x^8}\\ \end{align*}
Mathematica [A] time = 0.0049599, size = 43, normalized size = 1.08 \[ -\frac{3 b^2 c}{8 x^8}-\frac{b^3}{10 x^{10}}-\frac{b c^2}{2 x^6}-\frac{c^3}{4 x^4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.051, size = 36, normalized size = 0.9 \begin{align*} -{\frac{{b}^{3}}{10\,{x}^{10}}}-{\frac{{c}^{3}}{4\,{x}^{4}}}-{\frac{3\,{b}^{2}c}{8\,{x}^{8}}}-{\frac{b{c}^{2}}{2\,{x}^{6}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.960143, size = 50, normalized size = 1.25 \begin{align*} -\frac{10 \, c^{3} x^{6} + 20 \, b c^{2} x^{4} + 15 \, b^{2} c x^{2} + 4 \, b^{3}}{40 \, x^{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.40091, size = 85, normalized size = 2.12 \begin{align*} -\frac{10 \, c^{3} x^{6} + 20 \, b c^{2} x^{4} + 15 \, b^{2} c x^{2} + 4 \, b^{3}}{40 \, x^{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.481648, size = 39, normalized size = 0.98 \begin{align*} - \frac{4 b^{3} + 15 b^{2} c x^{2} + 20 b c^{2} x^{4} + 10 c^{3} x^{6}}{40 x^{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.21098, size = 50, normalized size = 1.25 \begin{align*} -\frac{10 \, c^{3} x^{6} + 20 \, b c^{2} x^{4} + 15 \, b^{2} c x^{2} + 4 \, b^{3}}{40 \, x^{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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