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 = 0.02, antiderivative size = 40, normalized size of antiderivative = 1.00, 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 37
Rule 45
Rule 266
Rule 1584
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*}
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Mathematica [A] time = 0.00, size = 43, normalized size = 1.08 \[ -\frac {b^3}{10 x^{10}}-\frac {3 b^2 c}{8 x^8}-\frac {b c^2}{2 x^6}-\frac {c^3}{4 x^4} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.70, size = 37, normalized size = 0.92 \[ -\frac {10 \, c^{3} x^{6} + 20 \, b c^{2} x^{4} + 15 \, b^{2} c x^{2} + 4 \, b^{3}}{40 \, x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 37, normalized size = 0.92 \[ -\frac {10 \, c^{3} x^{6} + 20 \, b c^{2} x^{4} + 15 \, b^{2} c x^{2} + 4 \, b^{3}}{40 \, x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 36, normalized size = 0.90 \[ -\frac {c^{3}}{4 x^{4}}-\frac {b \,c^{2}}{2 x^{6}}-\frac {3 b^{2} c}{8 x^{8}}-\frac {b^{3}}{10 x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.31, size = 37, normalized size = 0.92 \[ -\frac {10 \, c^{3} x^{6} + 20 \, b c^{2} x^{4} + 15 \, b^{2} c x^{2} + 4 \, b^{3}}{40 \, x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 37, normalized size = 0.92 \[ -\frac {\frac {b^3}{10}+\frac {3\,b^2\,c\,x^2}{8}+\frac {b\,c^2\,x^4}{2}+\frac {c^3\,x^6}{4}}{x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.32, size = 39, normalized size = 0.98 \[ \frac {- 4 b^{3} - 15 b^{2} c x^{2} - 20 b c^{2} x^{4} - 10 c^{3} x^{6}}{40 x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
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