Optimal. Leaf size=18 \[ -\frac {1}{7 b \left (a+b x^2\right )^{7/2}} \]
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Rubi [A] time = 0.00, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {261} \[ -\frac {1}{7 b \left (a+b x^2\right )^{7/2}} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin {align*} \int \frac {x}{\left (a+b x^2\right )^{9/2}} \, dx &=-\frac {1}{7 b \left (a+b x^2\right )^{7/2}}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 18, normalized size = 1.00 \[ -\frac {1}{7 b \left (a+b x^2\right )^{7/2}} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.87, size = 57, normalized size = 3.17 \[ -\frac {\sqrt {b x^{2} + a}}{7 \, {\left (b^{5} x^{8} + 4 \, a b^{4} x^{6} + 6 \, a^{2} b^{3} x^{4} + 4 \, a^{3} b^{2} x^{2} + a^{4} b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.97, size = 14, normalized size = 0.78 \[ -\frac {1}{7 \, {\left (b x^{2} + a\right )}^{\frac {7}{2}} b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 15, normalized size = 0.83 \[ -\frac {1}{7 \left (b \,x^{2}+a \right )^{\frac {7}{2}} b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.33, size = 14, normalized size = 0.78 \[ -\frac {1}{7 \, {\left (b x^{2} + a\right )}^{\frac {7}{2}} b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.60, size = 14, normalized size = 0.78 \[ -\frac {1}{7\,b\,{\left (b\,x^2+a\right )}^{7/2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 5.73, size = 90, normalized size = 5.00 \[ \begin {cases} - \frac {1}{7 a^{3} b \sqrt {a + b x^{2}} + 21 a^{2} b^{2} x^{2} \sqrt {a + b x^{2}} + 21 a b^{3} x^{4} \sqrt {a + b x^{2}} + 7 b^{4} x^{6} \sqrt {a + b x^{2}}} & \text {for}\: b \neq 0 \\\frac {x^{2}}{2 a^{\frac {9}{2}}} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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