Optimal. Leaf size=16 \[ -\frac {1}{21 x^{21} \left (b+c x^3\right )^7} \]
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Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.095, Rules used = {446, 74} \begin {gather*} -\frac {1}{21 x^{21} \left (b+c x^3\right )^7} \end {gather*}
Antiderivative was successfully verified.
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Rule 74
Rule 446
Rubi steps
\begin {align*} \int \frac {b+2 c x^3}{x^{22} \left (b+c x^3\right )^8} \, dx &=\frac {1}{3} \operatorname {Subst}\left (\int \frac {b+2 c x}{x^8 (b+c x)^8} \, dx,x,x^3\right )\\ &=-\frac {1}{21 x^{21} \left (b+c x^3\right )^7}\\ \end {align*}
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Mathematica [A] time = 0.05, size = 16, normalized size = 1.00 \begin {gather*} -\frac {1}{21 x^{21} \left (b+c x^3\right )^7} \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 {b+2 c x^3}{x^{22} \left (b+c x^3\right )^8} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 0.39, size = 81, normalized size = 5.06 \begin {gather*} -\frac {1}{21 \, {\left (c^{7} x^{42} + 7 \, b c^{6} x^{39} + 21 \, b^{2} c^{5} x^{36} + 35 \, b^{3} c^{4} x^{33} + 35 \, b^{4} c^{3} x^{30} + 21 \, b^{5} c^{2} x^{27} + 7 \, b^{6} c x^{24} + b^{7} x^{21}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 15, normalized size = 0.94 \begin {gather*} -\frac {1}{21 \, {\left (c x^{6} + b x^{3}\right )}^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.06, size = 197, normalized size = 12.31 \begin {gather*} -\frac {\left (-\frac {b^{6}}{7 \left (c \,x^{3}+b \right )^{7} c}-\frac {b^{5}}{\left (c \,x^{3}+b \right )^{6} c}-\frac {4 b^{4}}{\left (c \,x^{3}+b \right )^{5} c}-\frac {12 b^{3}}{\left (c \,x^{3}+b \right )^{4} c}-\frac {30 b^{2}}{\left (c \,x^{3}+b \right )^{3} c}-\frac {66 b}{\left (c \,x^{3}+b \right )^{2} c}-\frac {132}{\left (c \,x^{3}+b \right ) c}\right ) c^{8}}{3 b^{13}}-\frac {44 c^{6}}{b^{13} x^{3}}+\frac {22 c^{5}}{b^{12} x^{6}}-\frac {10 c^{4}}{b^{11} x^{9}}+\frac {4 c^{3}}{b^{10} x^{12}}-\frac {4 c^{2}}{3 b^{9} x^{15}}+\frac {c}{3 b^{8} x^{18}}-\frac {1}{21 b^{7} x^{21}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.61, size = 81, normalized size = 5.06 \begin {gather*} -\frac {1}{21 \, {\left (c^{7} x^{42} + 7 \, b c^{6} x^{39} + 21 \, b^{2} c^{5} x^{36} + 35 \, b^{3} c^{4} x^{33} + 35 \, b^{4} c^{3} x^{30} + 21 \, b^{5} c^{2} x^{27} + 7 \, b^{6} c x^{24} + b^{7} x^{21}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 9.98, size = 14, normalized size = 0.88 \begin {gather*} -\frac {1}{21\,x^{21}\,{\left (c\,x^3+b\right )}^7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 1.91, size = 87, normalized size = 5.44 \begin {gather*} - \frac {1}{21 b^{7} x^{21} + 147 b^{6} c x^{24} + 441 b^{5} c^{2} x^{27} + 735 b^{4} c^{3} x^{30} + 735 b^{3} c^{4} x^{33} + 441 b^{2} c^{5} x^{36} + 147 b c^{6} x^{39} + 21 c^{7} x^{42}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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