Optimal. Leaf size=23 \[ -\frac {32 x}{25}+\frac {2 x^2}{5}+\frac {121}{125} \log (3+5 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {45}
\begin {gather*} \frac {2 x^2}{5}-\frac {32 x}{25}+\frac {121}{125} \log (5 x+3) \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2}{3+5 x} \, dx &=\int \left (-\frac {32}{25}+\frac {4 x}{5}+\frac {121}{25 (3+5 x)}\right ) \, dx\\ &=-\frac {32 x}{25}+\frac {2 x^2}{5}+\frac {121}{125} \log (3+5 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 22, normalized size = 0.96 \begin {gather*} \frac {1}{125} \left (-114-160 x+50 x^2+121 \log (3+5 x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 18, normalized size = 0.78
method | result | size |
default | \(-\frac {32 x}{25}+\frac {2 x^{2}}{5}+\frac {121 \ln \left (3+5 x \right )}{125}\) | \(18\) |
norman | \(-\frac {32 x}{25}+\frac {2 x^{2}}{5}+\frac {121 \ln \left (3+5 x \right )}{125}\) | \(18\) |
risch | \(-\frac {32 x}{25}+\frac {2 x^{2}}{5}+\frac {121 \ln \left (3+5 x \right )}{125}\) | \(18\) |
meijerg | \(\frac {121 \ln \left (1+\frac {5 x}{3}\right )}{125}-\frac {4 x}{5}-\frac {2 x \left (-5 x +6\right )}{25}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 17, normalized size = 0.74 \begin {gather*} \frac {2}{5} \, x^{2} - \frac {32}{25} \, x + \frac {121}{125} \, \log \left (5 \, x + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 17, normalized size = 0.74 \begin {gather*} \frac {2}{5} \, x^{2} - \frac {32}{25} \, x + \frac {121}{125} \, \log \left (5 \, x + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 20, normalized size = 0.87 \begin {gather*} \frac {2 x^{2}}{5} - \frac {32 x}{25} + \frac {121 \log {\left (5 x + 3 \right )}}{125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.44, size = 18, normalized size = 0.78 \begin {gather*} \frac {2}{5} \, x^{2} - \frac {32}{25} \, x + \frac {121}{125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 15, normalized size = 0.65 \begin {gather*} \frac {121\,\ln \left (x+\frac {3}{5}\right )}{125}-\frac {32\,x}{25}+\frac {2\,x^2}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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