Optimal. Leaf size=19 \[ -\frac {\left (a+b x^2\right )^5}{10 a x^{10}} \]
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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 = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {28, 270}
\begin {gather*} -\frac {\left (a+b x^2\right )^5}{10 a x^{10}} \end {gather*}
Antiderivative was successfully verified.
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Rule 28
Rule 270
Rubi steps
\begin {align*} \int \frac {\left (a^2+2 a b x^2+b^2 x^4\right )^2}{x^{11}} \, dx &=\frac {\int \frac {\left (a b+b^2 x^2\right )^4}{x^{11}} \, dx}{b^4}\\ &=-\frac {\left (a+b x^2\right )^5}{10 a x^{10}}\\ \end {align*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(52\) vs. \(2(19)=38\).
time = 0.00, size = 52, normalized size = 2.74 \begin {gather*} -\frac {a^4}{10 x^{10}}-\frac {a^3 b}{2 x^8}-\frac {a^2 b^2}{x^6}-\frac {a b^3}{x^4}-\frac {b^4}{2 x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(46\) vs.
\(2(17)=34\).
time = 0.01, size = 47, normalized size = 2.47
method | result | size |
gosper | \(-\frac {5 b^{4} x^{8}+10 a \,b^{3} x^{6}+10 a^{2} b^{2} x^{4}+5 a^{3} b \,x^{2}+a^{4}}{10 x^{10}}\) | \(47\) |
default | \(-\frac {a \,b^{3}}{x^{4}}-\frac {b^{4}}{2 x^{2}}-\frac {a^{3} b}{2 x^{8}}-\frac {a^{4}}{10 x^{10}}-\frac {a^{2} b^{2}}{x^{6}}\) | \(47\) |
norman | \(\frac {-\frac {1}{2} b^{4} x^{8}-a \,b^{3} x^{6}-a^{2} b^{2} x^{4}-\frac {1}{2} a^{3} b \,x^{2}-\frac {1}{10} a^{4}}{x^{10}}\) | \(48\) |
risch | \(\frac {-\frac {1}{2} b^{4} x^{8}-a \,b^{3} x^{6}-a^{2} b^{2} x^{4}-\frac {1}{2} a^{3} b \,x^{2}-\frac {1}{10} a^{4}}{x^{10}}\) | \(48\) |
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. 46 vs.
\(2 (17) = 34\).
time = 0.38, size = 46, normalized size = 2.42 \begin {gather*} -\frac {5 \, b^{4} x^{8} + 10 \, a b^{3} x^{6} + 10 \, a^{2} b^{2} x^{4} + 5 \, a^{3} b x^{2} + a^{4}}{10 \, x^{10}} \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. 46 vs.
\(2 (17) = 34\).
time = 0.37, size = 46, normalized size = 2.42 \begin {gather*} -\frac {5 \, b^{4} x^{8} + 10 \, a b^{3} x^{6} + 10 \, a^{2} b^{2} x^{4} + 5 \, a^{3} b x^{2} + a^{4}}{10 \, x^{10}} \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. 49 vs.
\(2 (15) = 30\).
time = 0.16, size = 49, normalized size = 2.58 \begin {gather*} \frac {- a^{4} - 5 a^{3} b x^{2} - 10 a^{2} b^{2} x^{4} - 10 a b^{3} x^{6} - 5 b^{4} x^{8}}{10 x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 46 vs.
\(2 (17) = 34\).
time = 3.62, size = 46, normalized size = 2.42 \begin {gather*} -\frac {5 \, b^{4} x^{8} + 10 \, a b^{3} x^{6} + 10 \, a^{2} b^{2} x^{4} + 5 \, a^{3} b x^{2} + a^{4}}{10 \, x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 46, normalized size = 2.42 \begin {gather*} -\frac {\frac {a^4}{10}+\frac {a^3\,b\,x^2}{2}+a^2\,b^2\,x^4+a\,b^3\,x^6+\frac {b^4\,x^8}{2}}{x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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