Optimal. Leaf size=25 \[ 5-\frac {10}{x^2}+x+x^2+\frac {5}{\log (4) (3-\log (5))} \]
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Rubi [A]
time = 0.00, antiderivative size = 10, normalized size of antiderivative = 0.40, number of steps
used = 2, number of rules used = 1, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {14}
\begin {gather*} x^2-\frac {10}{x^2}+x \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1+\frac {20}{x^3}+2 x\right ) \, dx\\ &=-\frac {10}{x^2}+x+x^2\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 10, normalized size = 0.40 \begin {gather*} -\frac {10}{x^2}+x+x^2 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.13, size = 11, normalized size = 0.44
method | result | size |
default | \(x^{2}+x -\frac {10}{x^{2}}\) | \(11\) |
risch | \(x^{2}+x -\frac {10}{x^{2}}\) | \(11\) |
gosper | \(\frac {x^{4}+x^{3}-10}{x^{2}}\) | \(13\) |
norman | \(\frac {x^{4}+x^{3}-10}{x^{2}}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.25, size = 10, normalized size = 0.40 \begin {gather*} x^{2} + x - \frac {10}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 12, normalized size = 0.48 \begin {gather*} \frac {x^{4} + x^{3} - 10}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 8, normalized size = 0.32 \begin {gather*} x^{2} + x - \frac {10}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 10, normalized size = 0.40 \begin {gather*} x^{2} + x - \frac {10}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 12, normalized size = 0.48 \begin {gather*} \frac {x^4+x^3-10}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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