Optimal. Leaf size=16 \[ -\frac {25}{2 x^2}-x+(1+x)^2 \]
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Rubi [A] time = 0.00, antiderivative size = 12, normalized size of antiderivative = 0.75, 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 {25}{2 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 {25}{x^3}+2 x\right ) \, dx\\ &=-\frac {25}{2 x^2}+x+x^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 0.75 \begin {gather*} -\frac {25}{2 x^2}+x+x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.01, size = 17, normalized size = 1.06 \begin {gather*} \frac {2 \, x^{4} + 2 \, x^{3} - 25}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 10, normalized size = 0.62 \begin {gather*} x^{2} + x - \frac {25}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 11, normalized size = 0.69
method | result | size |
default | \(x^{2}+x -\frac {25}{2 x^{2}}\) | \(11\) |
risch | \(x^{2}+x -\frac {25}{2 x^{2}}\) | \(11\) |
norman | \(\frac {x^{4}+x^{3}-\frac {25}{2}}{x^{2}}\) | \(13\) |
gosper | \(\frac {2 x^{4}+2 x^{3}-25}{2 x^{2}}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 10, normalized size = 0.62 \begin {gather*} x^{2} + x - \frac {25}{2 \, 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 = 0.75 \begin {gather*} \frac {x^4+x^3-\frac {25}{2}}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 10, normalized size = 0.62 \begin {gather*} x^{2} + x - \frac {25}{2 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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