Optimal. Leaf size=25 \[ -\frac {x^{7/2}}{7 b \left (a x+b x^3\right )^{7/2}} \]
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Rubi [A]
time = 0.02, 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 = {2039}
\begin {gather*} -\frac {x^{7/2}}{7 b \left (a x+b x^3\right )^{7/2}} \end {gather*}
Antiderivative was successfully verified.
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Rule 2039
Rubi steps
\begin {align*} \int \frac {x^{11/2}}{\left (a x+b x^3\right )^{9/2}} \, dx &=-\frac {x^{7/2}}{7 b \left (a x+b x^3\right )^{7/2}}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 25, normalized size = 1.00 \begin {gather*} -\frac {x^{7/2}}{7 b \left (x \left (a+b x^2\right )\right )^{7/2}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.37, size = 29, normalized size = 1.16
method | result | size |
gosper | \(-\frac {\left (b \,x^{2}+a \right ) x^{\frac {9}{2}}}{7 b \left (b \,x^{3}+a x \right )^{\frac {9}{2}}}\) | \(27\) |
default | \(-\frac {\sqrt {x \left (b \,x^{2}+a \right )}}{7 \sqrt {x}\, \left (b \,x^{2}+a \right )^{4} b}\) | \(29\) |
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 \begin {gather*} \text {Failed to integrate} \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. 63 vs.
\(2 (19) = 38\).
time = 1.62, size = 63, normalized size = 2.52 \begin {gather*} -\frac {\sqrt {b x^{3} + a x} \sqrt {x}}{7 \, {\left (b^{5} x^{9} + 4 \, a b^{4} x^{7} + 6 \, a^{2} b^{3} x^{5} + 4 \, a^{3} b^{2} x^{3} + a^{4} b x\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x^{\frac {11}{2}}}{\left (x \left (a + b x^{2}\right )\right )^{\frac {9}{2}}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.96, size = 23, normalized size = 0.92 \begin {gather*} -\frac {1}{7 \, {\left (b x^{2} + a\right )}^{\frac {7}{2}} b} + \frac {1}{7 \, a^{\frac {7}{2}} b} \end {gather*}
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 \begin {gather*} \int \frac {x^{11/2}}{{\left (b\,x^3+a\,x\right )}^{9/2}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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