Optimal. Leaf size=27 \[ \frac {4 x}{25}-\frac {121}{125 (3+5 x)}-\frac {44}{125} \log (3+5 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 27, 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 {4 x}{25}-\frac {121}{125 (5 x+3)}-\frac {44}{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)^2} \, dx &=\int \left (\frac {4}{25}+\frac {121}{25 (3+5 x)^2}-\frac {44}{25 (3+5 x)}\right ) \, dx\\ &=\frac {4 x}{25}-\frac {121}{125 (3+5 x)}-\frac {44}{125} \log (3+5 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 34, normalized size = 1.26 \begin {gather*} \frac {-151+10 x+100 x^2-44 (3+5 x) \log (6+10 x)}{125 (3+5 x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 22, normalized size = 0.81
method | result | size |
risch | \(\frac {4 x}{25}-\frac {121}{625 \left (x +\frac {3}{5}\right )}-\frac {44 \ln \left (3+5 x \right )}{125}\) | \(20\) |
default | \(\frac {4 x}{25}-\frac {121}{125 \left (3+5 x \right )}-\frac {44 \ln \left (3+5 x \right )}{125}\) | \(22\) |
norman | \(\frac {\frac {157}{75} x +\frac {4}{5} x^{2}}{3+5 x}-\frac {44 \ln \left (3+5 x \right )}{125}\) | \(27\) |
meijerg | \(\frac {17 x}{45 \left (1+\frac {5 x}{3}\right )}-\frac {44 \ln \left (1+\frac {5 x}{3}\right )}{125}+\frac {4 x \left (5 x +6\right )}{75 \left (1+\frac {5 x}{3}\right )}\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 21, normalized size = 0.78 \begin {gather*} \frac {4}{25} \, x - \frac {121}{125 \, {\left (5 \, x + 3\right )}} - \frac {44}{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 = 0.39, size = 32, normalized size = 1.19 \begin {gather*} \frac {100 \, x^{2} - 44 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 60 \, x - 121}{125 \, {\left (5 \, x + 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 20, normalized size = 0.74 \begin {gather*} \frac {4 x}{25} - \frac {44 \log {\left (5 x + 3 \right )}}{125} - \frac {121}{625 x + 375} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.49, size = 32, normalized size = 1.19 \begin {gather*} \frac {4}{25} \, x - \frac {121}{125 \, {\left (5 \, x + 3\right )}} + \frac {44}{125} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) + \frac {12}{125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.08, size = 19, normalized size = 0.70 \begin {gather*} \frac {4\,x}{25}-\frac {44\,\ln \left (x+\frac {3}{5}\right )}{125}-\frac {121}{625\,\left (x+\frac {3}{5}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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