Optimal. Leaf size=16 \[ -\frac {1}{18 b \left (a+b x^2\right )^9} \]
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Rubi [A]
time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {267}
\begin {gather*} -\frac {1}{18 b \left (a+b x^2\right )^9} \end {gather*}
Antiderivative was successfully verified.
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Rule 267
Rubi steps
\begin {align*} \int \frac {x}{\left (a+b x^2\right )^{10}} \, dx &=-\frac {1}{18 b \left (a+b x^2\right )^9}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 16, normalized size = 1.00 \begin {gather*} -\frac {1}{18 b \left (a+b x^2\right )^9} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 15, normalized size = 0.94
method | result | size |
gosper | \(-\frac {1}{18 b \left (b \,x^{2}+a \right )^{9}}\) | \(15\) |
derivativedivides | \(-\frac {1}{18 b \left (b \,x^{2}+a \right )^{9}}\) | \(15\) |
default | \(-\frac {1}{18 b \left (b \,x^{2}+a \right )^{9}}\) | \(15\) |
norman | \(-\frac {1}{18 b \left (b \,x^{2}+a \right )^{9}}\) | \(15\) |
risch | \(-\frac {1}{18 b \left (b \,x^{2}+a \right )^{9}}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 14, normalized size = 0.88 \begin {gather*} -\frac {1}{18 \, {\left (b x^{2} + a\right )}^{9} b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 103 vs.
\(2 (14) = 28\).
time = 1.12, size = 103, normalized size = 6.44 \begin {gather*} -\frac {1}{18 \, {\left (b^{10} x^{18} + 9 \, a b^{9} x^{16} + 36 \, a^{2} b^{8} x^{14} + 84 \, a^{3} b^{7} x^{12} + 126 \, a^{4} b^{6} x^{10} + 126 \, a^{5} b^{5} x^{8} + 84 \, a^{6} b^{4} x^{6} + 36 \, a^{7} b^{3} x^{4} + 9 \, a^{8} b^{2} x^{2} + a^{9} b\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 110 vs.
\(2 (14) = 28\).
time = 0.40, size = 110, normalized size = 6.88 \begin {gather*} - \frac {1}{18 a^{9} b + 162 a^{8} b^{2} x^{2} + 648 a^{7} b^{3} x^{4} + 1512 a^{6} b^{4} x^{6} + 2268 a^{5} b^{5} x^{8} + 2268 a^{4} b^{6} x^{10} + 1512 a^{3} b^{7} x^{12} + 648 a^{2} b^{8} x^{14} + 162 a b^{9} x^{16} + 18 b^{10} x^{18}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.39, size = 14, normalized size = 0.88 \begin {gather*} -\frac {1}{18 \, {\left (b x^{2} + a\right )}^{9} b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.13, size = 14, normalized size = 0.88 \begin {gather*} -\frac {1}{18\,b\,{\left (b\,x^2+a\right )}^9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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