Optimal. Leaf size=52 \[ -\frac {2978 x}{3125}+\frac {354 x^2}{625}-\frac {24 x^3}{125}-\frac {1331}{31250 (3+5 x)^2}-\frac {1452}{3125 (3+5 x)}+\frac {1551 \log (3+5 x)}{3125} \]
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Rubi [A]
time = 0.02, antiderivative size = 52, 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 {24 x^3}{125}+\frac {354 x^2}{625}-\frac {2978 x}{3125}-\frac {1452}{3125 (5 x+3)}-\frac {1331}{31250 (5 x+3)^2}+\frac {1551 \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)^3 (2+3 x)^2}{(3+5 x)^3} \, dx &=\int \left (-\frac {2978}{3125}+\frac {708 x}{625}-\frac {72 x^2}{125}+\frac {1331}{3125 (3+5 x)^3}+\frac {1452}{625 (3+5 x)^2}+\frac {1551}{625 (3+5 x)}\right ) \, dx\\ &=-\frac {2978 x}{3125}+\frac {354 x^2}{625}-\frac {24 x^3}{125}-\frac {1331}{31250 (3+5 x)^2}-\frac {1452}{3125 (3+5 x)}+\frac {1551 \log (3+5 x)}{3125}\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 53, normalized size = 1.02 \begin {gather*} -\frac {54943+221340 x+274500 x^2+53500 x^3-52500 x^4+30000 x^5-3102 (3+5 x)^2 \log (6 (3+5 x))}{6250 (3+5 x)^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 41, normalized size = 0.79
method | result | size |
risch | \(-\frac {24 x^{3}}{125}+\frac {354 x^{2}}{625}-\frac {2978 x}{3125}+\frac {-\frac {1452 x}{625}-\frac {44891}{31250}}{\left (3+5 x \right )^{2}}+\frac {1551 \ln \left (3+5 x \right )}{3125}\) | \(37\) |
default | \(-\frac {2978 x}{3125}+\frac {354 x^{2}}{625}-\frac {24 x^{3}}{125}-\frac {1331}{31250 \left (3+5 x \right )^{2}}-\frac {1452}{3125 \left (3+5 x \right )}+\frac {1551 \ln \left (3+5 x \right )}{3125}\) | \(41\) |
norman | \(\frac {-\frac {11459}{1875} x -\frac {43877}{2250} x^{2}-\frac {214}{25} x^{3}+\frac {42}{5} x^{4}-\frac {24}{5} x^{5}}{\left (3+5 x \right )^{2}}+\frac {1551 \ln \left (3+5 x \right )}{3125}\) | \(42\) |
meijerg | \(\frac {2 x \left (\frac {5 x}{3}+2\right )}{27 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {2 x^{2}}{9 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {x \left (15 x +6\right )}{30 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {1551 \ln \left (1+\frac {5 x}{3}\right )}{3125}+\frac {29 x \left (\frac {100}{9} x^{2}+30 x +12\right )}{250 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {18 x \left (-\frac {625}{27} x^{3}+\frac {500}{9} x^{2}+150 x +60\right )}{3125 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {108 x \left (\frac {1250}{81} x^{4}-\frac {625}{27} x^{3}+\frac {500}{9} x^{2}+150 x +60\right )}{3125 \left (1+\frac {5 x}{3}\right )^{2}}\) | \(127\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 41, normalized size = 0.79 \begin {gather*} -\frac {24}{125} \, x^{3} + \frac {354}{625} \, x^{2} - \frac {2978}{3125} \, x - \frac {121 \, {\left (600 \, x + 371\right )}}{31250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac {1551}{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 = 0.41, size = 57, normalized size = 1.10 \begin {gather*} -\frac {150000 \, x^{5} - 262500 \, x^{4} + 267500 \, x^{3} + 734100 \, x^{2} - 15510 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 340620 \, x + 44891}{31250 \, {\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 = 0.05, size = 42, normalized size = 0.81 \begin {gather*} - \frac {24 x^{3}}{125} + \frac {354 x^{2}}{625} - \frac {2978 x}{3125} - \frac {72600 x + 44891}{781250 x^{2} + 937500 x + 281250} + \frac {1551 \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 = 0.68, size = 37, normalized size = 0.71 \begin {gather*} -\frac {24}{125} \, x^{3} + \frac {354}{625} \, x^{2} - \frac {2978}{3125} \, x - \frac {121 \, {\left (600 \, x + 371\right )}}{31250 \, {\left (5 \, x + 3\right )}^{2}} + \frac {1551}{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 = 0.03, size = 37, normalized size = 0.71 \begin {gather*} \frac {1551\,\ln \left (x+\frac {3}{5}\right )}{3125}-\frac {2978\,x}{3125}-\frac {\frac {1452\,x}{15625}+\frac {44891}{781250}}{x^2+\frac {6\,x}{5}+\frac {9}{25}}+\frac {354\,x^2}{625}-\frac {24\,x^3}{125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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