Optimal. Leaf size=38 \[ -\frac {75 x}{8}-\frac {1133}{16 (1-2 x)}+\frac {847}{32 (1-2 x)^2}-\frac {505}{16} \log (1-2 x) \]
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Rubi [A] time = 0.02, antiderivative size = 38, 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} \[ -\frac {75 x}{8}-\frac {1133}{16 (1-2 x)}+\frac {847}{32 (1-2 x)^2}-\frac {505}{16} \log (1-2 x) \]
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)^3} \, dx &=\int \left (-\frac {75}{8}-\frac {847}{8 (-1+2 x)^3}-\frac {1133}{8 (-1+2 x)^2}-\frac {505}{8 (-1+2 x)}\right ) \, dx\\ &=\frac {847}{32 (1-2 x)^2}-\frac {1133}{16 (1-2 x)}-\frac {75 x}{8}-\frac {505}{16} \log (1-2 x)\\ \end {align*}
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Mathematica [A] time = 0.03, size = 34, normalized size = 0.89 \[ \frac {1}{32} \left (\frac {600 x^2+3932 x-1269}{(1-2 x)^2}-300 x-1010 \log (1-2 x)\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 47, normalized size = 1.24 \[ -\frac {1200 \, x^{3} - 1200 \, x^{2} + 1010 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 4232 \, x + 1419}{32 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.16, size = 27, normalized size = 0.71 \[ -\frac {75}{8} \, x + \frac {11 \, {\left (412 \, x - 129\right )}}{32 \, {\left (2 \, x - 1\right )}^{2}} - \frac {505}{16} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 31, normalized size = 0.82 \[ -\frac {75 x}{8}-\frac {505 \ln \left (2 x -1\right )}{16}+\frac {847}{32 \left (2 x -1\right )^{2}}+\frac {1133}{16 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 31, normalized size = 0.82 \[ -\frac {75}{8} \, x + \frac {11 \, {\left (412 \, x - 129\right )}}{32 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {505}{16} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 26, normalized size = 0.68 \[ \frac {\frac {1133\,x}{32}-\frac {1419}{128}}{x^2-x+\frac {1}{4}}-\frac {505\,\ln \left (x-\frac {1}{2}\right )}{16}-\frac {75\,x}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 31, normalized size = 0.82 \[ - \frac {75 x}{8} - \frac {1419 - 4532 x}{128 x^{2} - 128 x + 32} - \frac {505 \log {\left (2 x - 1 \right )}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
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