Optimal. Leaf size=38 \[ -\frac {50 x}{27}+\frac {8}{9 (3 x+2)}-\frac {7}{162 (3 x+2)^2}+\frac {65}{27} \log (3 x+2) \]
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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} \[ -\frac {50 x}{27}+\frac {8}{9 (3 x+2)}-\frac {7}{162 (3 x+2)^2}+\frac {65}{27} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(1-2 x) (3+5 x)^2}{(2+3 x)^3} \, dx &=\int \left (-\frac {50}{27}+\frac {7}{27 (2+3 x)^3}-\frac {8}{3 (2+3 x)^2}+\frac {65}{9 (2+3 x)}\right ) \, dx\\ &=-\frac {50 x}{27}-\frac {7}{162 (2+3 x)^2}+\frac {8}{9 (2+3 x)}+\frac {65}{27} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.03, size = 35, normalized size = 0.92 \[ \frac {1}{162} \left (-\frac {3 \left (600 x^2+656 x+173\right )}{(3 x+2)^2}-300 x+390 \log (3 x+2)\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.56, size = 47, normalized size = 1.24 \[ -\frac {2700 \, x^{3} + 3600 \, x^{2} - 390 \, {\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) + 768 \, x - 281}{162 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.18, size = 27, normalized size = 0.71 \[ -\frac {50}{27} \, x + \frac {432 \, x + 281}{162 \, {\left (3 \, x + 2\right )}^{2}} + \frac {65}{27} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
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 \[ -\frac {50 x}{27}+\frac {65 \ln \left (3 x +2\right )}{27}-\frac {7}{162 \left (3 x +2\right )^{2}}+\frac {8}{9 \left (3 x +2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 31, normalized size = 0.82 \[ -\frac {50}{27} \, x + \frac {432 \, x + 281}{162 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} + \frac {65}{27} \, \log \left (3 \, x + 2\right ) \]
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 \[ \frac {65\,\ln \left (x+\frac {2}{3}\right )}{27}-\frac {50\,x}{27}+\frac {\frac {8\,x}{27}+\frac {281}{1458}}{x^2+\frac {4\,x}{3}+\frac {4}{9}} \]
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 \[ - \frac {50 x}{27} - \frac {- 432 x - 281}{1458 x^{2} + 1944 x + 648} + \frac {65 \log {\left (3 x + 2 \right )}}{27} \]
Verification of antiderivative is not currently implemented for this CAS.
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