Optimal. Leaf size=41 \[ \frac {37 x}{625}-\frac {78 x^2}{125}+\frac {12 x^3}{25}-\frac {121}{3125 (3+5 x)}+\frac {682 \log (3+5 x)}{3125} \]
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Rubi [A]
time = 0.01, antiderivative size = 41, 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 {12 x^3}{25}-\frac {78 x^2}{125}+\frac {37 x}{625}-\frac {121}{3125 (5 x+3)}+\frac {682 \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)^2} \, dx &=\int \left (\frac {37}{625}-\frac {156 x}{125}+\frac {36 x^2}{25}+\frac {121}{625 (3+5 x)^2}+\frac {682}{625 (3+5 x)}\right ) \, dx\\ &=\frac {37 x}{625}-\frac {78 x^2}{125}+\frac {12 x^3}{25}-\frac {121}{3125 (3+5 x)}+\frac {682 \log (3+5 x)}{3125}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 42, normalized size = 1.02 \begin {gather*} \frac {\frac {5 \left (658+1248 x-985 x^2-1050 x^3+1500 x^4\right )}{3+5 x}+682 \log (3+5 x)}{3125} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 32, normalized size = 0.78
method | result | size |
risch | \(\frac {12 x^{3}}{25}-\frac {78 x^{2}}{125}+\frac {37 x}{625}-\frac {121}{15625 \left (x +\frac {3}{5}\right )}+\frac {682 \ln \left (3+5 x \right )}{3125}\) | \(30\) |
default | \(\frac {37 x}{625}-\frac {78 x^{2}}{125}+\frac {12 x^{3}}{25}-\frac {121}{3125 \left (3+5 x \right )}+\frac {682 \ln \left (3+5 x \right )}{3125}\) | \(32\) |
norman | \(\frac {\frac {454}{1875} x -\frac {197}{125} x^{2}-\frac {42}{25} x^{3}+\frac {12}{5} x^{4}}{3+5 x}+\frac {682 \ln \left (3+5 x \right )}{3125}\) | \(37\) |
meijerg | \(\frac {32 x}{45 \left (1+\frac {5 x}{3}\right )}+\frac {682 \ln \left (1+\frac {5 x}{3}\right )}{3125}-\frac {23 x \left (5 x +6\right )}{75 \left (1+\frac {5 x}{3}\right )}-\frac {9 x \left (-\frac {50}{9} x^{2}+10 x +12\right )}{125 \left (1+\frac {5 x}{3}\right )}+\frac {108 x \left (\frac {625}{27} x^{3}-\frac {250}{9} x^{2}+50 x +60\right )}{3125 \left (1+\frac {5 x}{3}\right )}\) | \(80\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 31, normalized size = 0.76 \begin {gather*} \frac {12}{25} \, x^{3} - \frac {78}{125} \, x^{2} + \frac {37}{625} \, x - \frac {121}{3125 \, {\left (5 \, x + 3\right )}} + \frac {682}{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 = 0.49, size = 42, normalized size = 1.02 \begin {gather*} \frac {7500 \, x^{4} - 5250 \, x^{3} - 4925 \, x^{2} + 682 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 555 \, x - 121}{3125 \, {\left (5 \, x + 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 34, normalized size = 0.83 \begin {gather*} \frac {12 x^{3}}{25} - \frac {78 x^{2}}{125} + \frac {37 x}{625} + \frac {682 \log {\left (5 x + 3 \right )}}{3125} - \frac {121}{15625 x + 9375} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.31, size = 57, normalized size = 1.39 \begin {gather*} -\frac {1}{3125} \, {\left (5 \, x + 3\right )}^{3} {\left (\frac {186}{5 \, x + 3} - \frac {829}{{\left (5 \, x + 3\right )}^{2}} - 12\right )} - \frac {121}{3125 \, {\left (5 \, x + 3\right )}} - \frac {682}{3125} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 29, normalized size = 0.71 \begin {gather*} \frac {37\,x}{625}+\frac {682\,\ln \left (x+\frac {3}{5}\right )}{3125}-\frac {121}{15625\,\left (x+\frac {3}{5}\right )}-\frac {78\,x^2}{125}+\frac {12\,x^3}{25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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