Optimal. Leaf size=27 \[ \frac {4 x}{25}-\frac {121}{125 (5 x+3)}-\frac {44}{125} \log (5 x+3) \]
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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 = {43} \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 43
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 {100 x^2+10 x-44 (5 x+3) \log (10 x+6)-151}{125 (5 x+3)} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(1-2 x)^2}{(3+5 x)^2} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.30, 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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giac [A] time = 0.97, 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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maple [A] time = 0.01, size = 22, normalized size = 0.81 \begin {gather*} \frac {4 x}{25}-\frac {44 \ln \left (5 x +3\right )}{125}-\frac {121}{125 \left (5 x +3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, 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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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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sympy [A] time = 0.10, 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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