Optimal. Leaf size=25 \[ \frac {x^{21/2}}{7 a \left (a x+b x^3\right )^{7/2}} \]
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Rubi [A] time = 0.04, antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {2014} \[ \frac {x^{21/2}}{7 a \left (a x+b x^3\right )^{7/2}} \]
Antiderivative was successfully verified.
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Rule 2014
Rubi steps
\begin {align*} \int \frac {x^{21/2}}{\left (a x+b x^3\right )^{9/2}} \, dx &=\frac {x^{21/2}}{7 a \left (a x+b x^3\right )^{7/2}}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 25, normalized size = 1.00 \[ \frac {x^{21/2}}{7 a \left (x \left (a+b x^2\right )\right )^{7/2}} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.49, size = 61, normalized size = 2.44 \[ \frac {\sqrt {b x^{3} + a x} x^{\frac {13}{2}}}{7 \, {\left (a b^{4} x^{8} + 4 \, a^{2} b^{3} x^{6} + 6 \, a^{3} b^{2} x^{4} + 4 \, a^{4} b x^{2} + a^{5}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.29, size = 17, normalized size = 0.68 \[ \frac {x^{7}}{7 \, {\left (b x^{2} + a\right )}^{\frac {7}{2}} a} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 27, normalized size = 1.08 \[ \frac {\left (b \,x^{2}+a \right ) x^{\frac {23}{2}}}{7 \left (b \,x^{3}+a x \right )^{\frac {9}{2}} a} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {x^{\frac {21}{2}}}{{\left (b x^{3} + a x\right )}^{\frac {9}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {x^{21/2}}{{\left (b\,x^3+a\,x\right )}^{9/2}} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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