Optimal. Leaf size=30 \[ -\frac {25 x^3}{2}-\frac {355 x^2}{8}-\frac {703 x}{8}-\frac {847}{16} \log (1-2 x) \]
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Rubi [A] time = 0.01, antiderivative size = 30, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \[ -\frac {25 x^3}{2}-\frac {355 x^2}{8}-\frac {703 x}{8}-\frac {847}{16} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(2+3 x) (3+5 x)^2}{1-2 x} \, dx &=\int \left (-\frac {703}{8}-\frac {355 x}{4}-\frac {75 x^2}{2}-\frac {847}{8 (-1+2 x)}\right ) \, dx\\ &=-\frac {703 x}{8}-\frac {355 x^2}{8}-\frac {25 x^3}{2}-\frac {847}{16} \log (1-2 x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 27, normalized size = 0.90 \[ \frac {1}{32} \left (-400 x^3-1420 x^2-2812 x-1694 \log (1-2 x)+1811\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.86, size = 22, normalized size = 0.73 \[ -\frac {25}{2} \, x^{3} - \frac {355}{8} \, x^{2} - \frac {703}{8} \, x - \frac {847}{16} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.89, size = 23, normalized size = 0.77 \[ -\frac {25}{2} \, x^{3} - \frac {355}{8} \, x^{2} - \frac {703}{8} \, x - \frac {847}{16} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 23, normalized size = 0.77 \[ -\frac {25 x^{3}}{2}-\frac {355 x^{2}}{8}-\frac {703 x}{8}-\frac {847 \ln \left (2 x -1\right )}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 22, normalized size = 0.73 \[ -\frac {25}{2} \, x^{3} - \frac {355}{8} \, x^{2} - \frac {703}{8} \, x - \frac {847}{16} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 20, normalized size = 0.67 \[ -\frac {703\,x}{8}-\frac {847\,\ln \left (x-\frac {1}{2}\right )}{16}-\frac {355\,x^2}{8}-\frac {25\,x^3}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 29, normalized size = 0.97 \[ - \frac {25 x^{3}}{2} - \frac {355 x^{2}}{8} - \frac {703 x}{8} - \frac {847 \log {\left (2 x - 1 \right )}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
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