Optimal. Leaf size=15 \[ -x+\log \left (9-2 \left (-4+x+x^2\right )\right ) \]
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Rubi [A]
time = 0.02, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.087, Rules used = {1671, 642}
\begin {gather*} \log \left (-2 x^2-2 x+17\right )-x \end {gather*}
Antiderivative was successfully verified.
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Rule 642
Rule 1671
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-1+\frac {2 (1+2 x)}{-17+2 x+2 x^2}\right ) \, dx\\ &=-x+2 \int \frac {1+2 x}{-17+2 x+2 x^2} \, dx\\ &=-x+\log \left (17-2 x-2 x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 15, normalized size = 1.00 \begin {gather*} -x+\log \left (17-2 x-2 x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.74, size = 16, normalized size = 1.07
method | result | size |
default | \(-x +\ln \left (2 x^{2}+2 x -17\right )\) | \(16\) |
norman | \(-x +\ln \left (2 x^{2}+2 x -17\right )\) | \(16\) |
risch | \(-x +\ln \left (2 x^{2}+2 x -17\right )\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 15, normalized size = 1.00 \begin {gather*} -x + \log \left (2 \, x^{2} + 2 \, x - 17\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 15, normalized size = 1.00 \begin {gather*} -x + \log \left (2 \, x^{2} + 2 \, x - 17\right ) \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 = 0.80 \begin {gather*} - x + \log {\left (2 x^{2} + 2 x - 17 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 16, normalized size = 1.07 \begin {gather*} -x + \log \left ({\left | 2 \, x^{2} + 2 \, x - 17 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 11, normalized size = 0.73 \begin {gather*} \ln \left (x^2+x-\frac {17}{2}\right )-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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