Optimal. Leaf size=16 \[ \frac {1}{4} \left (-5-\frac {1}{x}-x+\log (x)\right ) \]
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Rubi [A]
time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.19, number of steps
used = 3, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {12, 14}
\begin {gather*} -\frac {x}{4}-\frac {1}{4 x}+\frac {\log (x)}{4} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int \frac {1+x-x^2}{x^2} \, dx\\ &=\frac {1}{4} \int \left (-1+\frac {1}{x^2}+\frac {1}{x}\right ) \, dx\\ &=-\frac {1}{4 x}-\frac {x}{4}+\frac {\log (x)}{4}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 15, normalized size = 0.94 \begin {gather*} \frac {1}{4} \left (-\frac {1}{x}-x+\log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.05, size = 14, normalized size = 0.88
method | result | size |
default | \(-\frac {x}{4}-\frac {1}{4 x}+\frac {\ln \left (x \right )}{4}\) | \(14\) |
risch | \(-\frac {x}{4}-\frac {1}{4 x}+\frac {\ln \left (x \right )}{4}\) | \(14\) |
norman | \(\frac {-\frac {1}{4}-\frac {x^{2}}{4}}{x}+\frac {\ln \left (x \right )}{4}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 13, normalized size = 0.81 \begin {gather*} -\frac {1}{4} \, x - \frac {1}{4 \, x} + \frac {1}{4} \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 15, normalized size = 0.94 \begin {gather*} -\frac {x^{2} - x \log \left (x\right ) + 1}{4 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 12, normalized size = 0.75 \begin {gather*} - \frac {x}{4} + \frac {\log {\left (x \right )}}{4} - \frac {1}{4 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 14, normalized size = 0.88 \begin {gather*} -\frac {1}{4} \, x - \frac {1}{4 \, x} + \frac {1}{4} \, \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 13, normalized size = 0.81 \begin {gather*} \frac {\ln \left (x\right )}{4}-\frac {x}{4}-\frac {1}{4\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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