Optimal. Leaf size=16 \[ -\frac {1}{14 x^{14} \left (b+c x^2\right )^7} \]
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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}{14 x^{14} \left (b+c x^2\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^2}{x^{15} \left (b+c x^2\right )^8} \, dx &=\frac {1}{2} \operatorname {Subst}\left (\int \frac {b+2 c x}{x^8 (b+c x)^8} \, dx,x,x^2\right )\\ &=-\frac {1}{14 x^{14} \left (b+c x^2\right )^7}\\ \end {align*}
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Mathematica [A] time = 0.05, size = 16, normalized size = 1.00 \begin {gather*} -\frac {1}{14 x^{14} \left (b+c x^2\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^2}{x^{15} \left (b+c x^2\right )^8} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 0.41, size = 81, normalized size = 5.06 \begin {gather*} -\frac {1}{14 \, {\left (c^{7} x^{28} + 7 \, b c^{6} x^{26} + 21 \, b^{2} c^{5} x^{24} + 35 \, b^{3} c^{4} x^{22} + 35 \, b^{4} c^{3} x^{20} + 21 \, b^{5} c^{2} x^{18} + 7 \, b^{6} c x^{16} + b^{7} x^{14}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 15, normalized size = 0.94 \begin {gather*} -\frac {1}{14 \, {\left (c x^{4} + b x^{2}\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^{2}+b \right )^{7} c}-\frac {b^{5}}{\left (c \,x^{2}+b \right )^{6} c}-\frac {4 b^{4}}{\left (c \,x^{2}+b \right )^{5} c}-\frac {12 b^{3}}{\left (c \,x^{2}+b \right )^{4} c}-\frac {30 b^{2}}{\left (c \,x^{2}+b \right )^{3} c}-\frac {66 b}{\left (c \,x^{2}+b \right )^{2} c}-\frac {132}{\left (c \,x^{2}+b \right ) c}\right ) c^{8}}{2 b^{13}}-\frac {66 c^{6}}{b^{13} x^{2}}+\frac {33 c^{5}}{b^{12} x^{4}}-\frac {15 c^{4}}{b^{11} x^{6}}+\frac {6 c^{3}}{b^{10} x^{8}}-\frac {2 c^{2}}{b^{9} x^{10}}+\frac {c}{2 b^{8} x^{12}}-\frac {1}{14 b^{7} x^{14}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.64, size = 81, normalized size = 5.06 \begin {gather*} -\frac {1}{14 \, {\left (c^{7} x^{28} + 7 \, b c^{6} x^{26} + 21 \, b^{2} c^{5} x^{24} + 35 \, b^{3} c^{4} x^{22} + 35 \, b^{4} c^{3} x^{20} + 21 \, b^{5} c^{2} x^{18} + 7 \, b^{6} c x^{16} + b^{7} x^{14}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.32, size = 14, normalized size = 0.88 \begin {gather*} -\frac {1}{14\,x^{14}\,{\left (c\,x^2+b\right )}^7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 1.36, size = 87, normalized size = 5.44 \begin {gather*} - \frac {1}{14 b^{7} x^{14} + 98 b^{6} c x^{16} + 294 b^{5} c^{2} x^{18} + 490 b^{4} c^{3} x^{20} + 490 b^{3} c^{4} x^{22} + 294 b^{2} c^{5} x^{24} + 98 b c^{6} x^{26} + 14 c^{7} x^{28}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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