Optimal. Leaf size=19 \[ \frac {x^{10}}{10 b \left (b+a x^5\right )^2} \]
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Rubi [A]
time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {1607, 270}
\begin {gather*} \frac {x^{10}}{10 b \left (a x^5+b\right )^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 270
Rule 1607
Rubi steps
\begin {align*} \int \frac {1}{\left (\frac {b}{x^3}+a x^2\right )^3} \, dx &=\int \frac {x^9}{\left (b+a x^5\right )^3} \, dx\\ &=\frac {x^{10}}{10 b \left (b+a x^5\right )^2}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 24, normalized size = 1.26 \begin {gather*} -\frac {b+2 a x^5}{10 a^2 \left (b+a x^5\right )^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.05, size = 31, normalized size = 1.63
method | result | size |
gosper | \(-\frac {2 a \,x^{5}+b}{10 \left (a \,x^{5}+b \right )^{2} a^{2}}\) | \(23\) |
norman | \(\frac {-\frac {x^{5}}{5 a}-\frac {b}{10 a^{2}}}{\left (a \,x^{5}+b \right )^{2}}\) | \(26\) |
risch | \(\frac {-\frac {x^{5}}{5 a}-\frac {b}{10 a^{2}}}{\left (a \,x^{5}+b \right )^{2}}\) | \(26\) |
default | \(-\frac {1}{5 a^{2} \left (a \,x^{5}+b \right )}+\frac {b}{10 a^{2} \left (a \,x^{5}+b \right )^{2}}\) | \(31\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 36 vs.
\(2 (17) = 34\).
time = 0.29, size = 36, normalized size = 1.89 \begin {gather*} -\frac {2 \, a x^{5} + b}{10 \, {\left (a^{4} x^{10} + 2 \, a^{3} b x^{5} + a^{2} b^{2}\right )}} \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. 36 vs.
\(2 (17) = 34\).
time = 2.50, size = 36, normalized size = 1.89 \begin {gather*} -\frac {2 \, a x^{5} + b}{10 \, {\left (a^{4} x^{10} + 2 \, a^{3} b x^{5} + a^{2} b^{2}\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. 36 vs.
\(2 (14) = 28\).
time = 0.22, size = 36, normalized size = 1.89 \begin {gather*} \frac {- 2 a x^{5} - b}{10 a^{4} x^{10} + 20 a^{3} b x^{5} + 10 a^{2} b^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.59, size = 22, normalized size = 1.16 \begin {gather*} -\frac {2 \, a x^{5} + b}{10 \, {\left (a x^{5} + b\right )}^{2} a^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.06, size = 37, normalized size = 1.95 \begin {gather*} -\frac {\frac {b}{10\,a^2}+\frac {x^5}{5\,a}}{a^2\,x^{10}+2\,a\,b\,x^5+b^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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