Optimal. Leaf size=21 \[ \frac {x^7}{7 a \left (a+b x^2\right )^{7/2}} \]
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Rubi [A] time = 0.00, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {264} \[ \frac {x^7}{7 a \left (a+b x^2\right )^{7/2}} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin {align*} \int \frac {x^6}{\left (a+b x^2\right )^{9/2}} \, dx &=\frac {x^7}{7 a \left (a+b x^2\right )^{7/2}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 21, normalized size = 1.00 \[ \frac {x^7}{7 a \left (a+b x^2\right )^{7/2}} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.62, size = 59, normalized size = 2.81 \[ \frac {\sqrt {b x^{2} + a} x^{7}}{7 \, {\left (a b^{4} x^{8} + 4 \, a^{2} b^{3} x^{6} + 6 \, a^{3} b^{2} x^{4} + 4 \, a^{4} b x^{2} + a^{5}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.22, size = 17, normalized size = 0.81 \[ \frac {x^{7}}{7 \, {\left (b x^{2} + a\right )}^{\frac {7}{2}} a} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 18, normalized size = 0.86 \[ \frac {x^{7}}{7 \left (b \,x^{2}+a \right )^{\frac {7}{2}} a} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.33, size = 103, normalized size = 4.90 \[ -\frac {x^{5}}{2 \, {\left (b x^{2} + a\right )}^{\frac {7}{2}} b} - \frac {5 \, a x^{3}}{8 \, {\left (b x^{2} + a\right )}^{\frac {7}{2}} b^{2}} + \frac {x}{14 \, {\left (b x^{2} + a\right )}^{\frac {3}{2}} b^{3}} + \frac {x}{7 \, \sqrt {b x^{2} + a} a b^{3}} + \frac {3 \, a x}{56 \, {\left (b x^{2} + a\right )}^{\frac {5}{2}} b^{3}} - \frac {15 \, a^{2} x}{56 \, {\left (b x^{2} + a\right )}^{\frac {7}{2}} b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.76, size = 68, normalized size = 3.24 \[ \frac {x}{7\,a\,b^3\,\sqrt {b\,x^2+a}}-\frac {3\,x}{7\,b^3\,{\left (b\,x^2+a\right )}^{3/2}}-\frac {a^2\,x}{7\,b^3\,{\left (b\,x^2+a\right )}^{7/2}}+\frac {3\,a\,x}{7\,b^3\,{\left (b\,x^2+a\right )}^{5/2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 1.47, size = 95, normalized size = 4.52 \[ \frac {x^{7}}{7 a^{\frac {9}{2}} \sqrt {1 + \frac {b x^{2}}{a}} + 21 a^{\frac {7}{2}} b x^{2} \sqrt {1 + \frac {b x^{2}}{a}} + 21 a^{\frac {5}{2}} b^{2} x^{4} \sqrt {1 + \frac {b x^{2}}{a}} + 7 a^{\frac {3}{2}} b^{3} x^{6} \sqrt {1 + \frac {b x^{2}}{a}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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