Optimal. Leaf size=45 \[ -\frac {264 x}{625}+\frac {18 x^2}{125}-\frac {121}{6250 (3+5 x)^2}-\frac {682}{3125 (3+5 x)}+\frac {829 \log (3+5 x)}{3125} \]
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Rubi [A]
time = 0.01, antiderivative size = 45, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90}
\begin {gather*} \frac {18 x^2}{125}-\frac {264 x}{625}-\frac {682}{3125 (5 x+3)}-\frac {121}{6250 (5 x+3)^2}+\frac {829 \log (5 x+3)}{3125} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2 (2+3 x)^2}{(3+5 x)^3} \, dx &=\int \left (-\frac {264}{625}+\frac {36 x}{125}+\frac {121}{625 (3+5 x)^3}+\frac {682}{625 (3+5 x)^2}+\frac {829}{625 (3+5 x)}\right ) \, dx\\ &=-\frac {264 x}{625}+\frac {18 x^2}{125}-\frac {121}{6250 (3+5 x)^2}-\frac {682}{3125 (3+5 x)}+\frac {829 \log (3+5 x)}{3125}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 42, normalized size = 0.93 \begin {gather*} \frac {\frac {5 \left (-4277-17564 x-23760 x^2-7800 x^3+4500 x^4\right )}{(3+5 x)^2}+1658 \log (3+5 x)}{6250} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 36, normalized size = 0.80
method | result | size |
risch | \(\frac {18 x^{2}}{125}-\frac {264 x}{625}+\frac {-\frac {682 x}{625}-\frac {4213}{6250}}{\left (3+5 x \right )^{2}}+\frac {829 \ln \left (3+5 x \right )}{3125}\) | \(32\) |
default | \(-\frac {264 x}{625}+\frac {18 x^{2}}{125}-\frac {121}{6250 \left (3+5 x \right )^{2}}-\frac {682}{3125 \left (3+5 x \right )}+\frac {829 \ln \left (3+5 x \right )}{3125}\) | \(36\) |
norman | \(\frac {-\frac {4961}{1875} x -\frac {21383}{2250} x^{2}-\frac {156}{25} x^{3}+\frac {18}{5} x^{4}}{\left (3+5 x \right )^{2}}+\frac {829 \ln \left (3+5 x \right )}{3125}\) | \(37\) |
meijerg | \(\frac {2 x \left (\frac {5 x}{3}+2\right )}{27 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {2 x^{2}}{27 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {23 x \left (15 x +6\right )}{450 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {829 \ln \left (1+\frac {5 x}{3}\right )}{3125}+\frac {3 x \left (\frac {100}{9} x^{2}+30 x +12\right )}{125 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {54 x \left (-\frac {625}{27} x^{3}+\frac {500}{9} x^{2}+150 x +60\right )}{3125 \left (1+\frac {5 x}{3}\right )^{2}}\) | \(97\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 36, normalized size = 0.80 \begin {gather*} \frac {18}{125} \, x^{2} - \frac {264}{625} \, x - \frac {11 \, {\left (620 \, x + 383\right )}}{6250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac {829}{3125} \, \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 = 0.42, size = 52, normalized size = 1.16 \begin {gather*} \frac {22500 \, x^{4} - 39000 \, x^{3} - 71100 \, x^{2} + 1658 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 30580 \, x - 4213}{6250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 37, normalized size = 0.82 \begin {gather*} \frac {18 x^{2}}{125} - \frac {264 x}{625} + \frac {- 6820 x - 4213}{156250 x^{2} + 187500 x + 56250} + \frac {829 \log {\left (5 x + 3 \right )}}{3125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.70, size = 32, normalized size = 0.71 \begin {gather*} \frac {18}{125} \, x^{2} - \frac {264}{625} \, x - \frac {11 \, {\left (620 \, x + 383\right )}}{6250 \, {\left (5 \, x + 3\right )}^{2}} + \frac {829}{3125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 32, normalized size = 0.71 \begin {gather*} \frac {829\,\ln \left (x+\frac {3}{5}\right )}{3125}-\frac {264\,x}{625}-\frac {\frac {682\,x}{15625}+\frac {4213}{156250}}{x^2+\frac {6\,x}{5}+\frac {9}{25}}+\frac {18\,x^2}{125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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