Optimal. Leaf size=48 \[ \frac {2416 x}{3125}-\frac {1449 x^2}{1250}-\frac {36 x^3}{125}+\frac {27 x^4}{25}-\frac {121}{15625 (3+5 x)}+\frac {209 \log (3+5 x)}{3125} \]
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Rubi [A]
time = 0.01, antiderivative size = 48, 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 {27 x^4}{25}-\frac {36 x^3}{125}-\frac {1449 x^2}{1250}+\frac {2416 x}{3125}-\frac {121}{15625 (5 x+3)}+\frac {209 \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)^3}{(3+5 x)^2} \, dx &=\int \left (\frac {2416}{3125}-\frac {1449 x}{625}-\frac {108 x^2}{125}+\frac {108 x^3}{25}+\frac {121}{3125 (3+5 x)^2}+\frac {209}{625 (3+5 x)}\right ) \, dx\\ &=\frac {2416 x}{3125}-\frac {1449 x^2}{1250}-\frac {36 x^3}{125}+\frac {27 x^4}{25}-\frac {121}{15625 (3+5 x)}+\frac {209 \log (3+5 x)}{3125}\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 51, normalized size = 1.06 \begin {gather*} \frac {12683+35715 x+2425 x^2-41625 x^3+11250 x^4+33750 x^5+418 (3+5 x) \log (6 (3+5 x))}{6250 (3+5 x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 37, normalized size = 0.77
method | result | size |
risch | \(\frac {27 x^{4}}{25}-\frac {36 x^{3}}{125}-\frac {1449 x^{2}}{1250}+\frac {2416 x}{3125}-\frac {121}{78125 \left (x +\frac {3}{5}\right )}+\frac {209 \ln \left (3+5 x \right )}{3125}\) | \(35\) |
default | \(\frac {2416 x}{3125}-\frac {1449 x^{2}}{1250}-\frac {36 x^{3}}{125}+\frac {27 x^{4}}{25}-\frac {121}{15625 \left (3+5 x \right )}+\frac {209 \ln \left (3+5 x \right )}{3125}\) | \(37\) |
norman | \(\frac {\frac {4373}{1875} x +\frac {97}{250} x^{2}-\frac {333}{50} x^{3}+\frac {9}{5} x^{4}+\frac {27}{5} x^{5}}{3+5 x}+\frac {209 \ln \left (3+5 x \right )}{3125}\) | \(42\) |
meijerg | \(\frac {28 x}{45 \left (1+\frac {5 x}{3}\right )}+\frac {209 \ln \left (1+\frac {5 x}{3}\right )}{3125}-\frac {58 x \left (5 x +6\right )}{75 \left (1+\frac {5 x}{3}\right )}+\frac {27 x \left (-\frac {50}{9} x^{2}+10 x +12\right )}{100 \left (1+\frac {5 x}{3}\right )}+\frac {324 x \left (\frac {625}{27} x^{3}-\frac {250}{9} x^{2}+50 x +60\right )}{3125 \left (1+\frac {5 x}{3}\right )}-\frac {243 x \left (-\frac {625}{27} x^{4}+\frac {625}{27} x^{3}-\frac {250}{9} x^{2}+50 x +60\right )}{3125 \left (1+\frac {5 x}{3}\right )}\) | \(110\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.33, size = 36, normalized size = 0.75 \begin {gather*} \frac {27}{25} \, x^{4} - \frac {36}{125} \, x^{3} - \frac {1449}{1250} \, x^{2} + \frac {2416}{3125} \, x - \frac {121}{15625 \, {\left (5 \, x + 3\right )}} + \frac {209}{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 = 0.47, size = 47, normalized size = 0.98 \begin {gather*} \frac {168750 \, x^{5} + 56250 \, x^{4} - 208125 \, x^{3} + 12125 \, x^{2} + 2090 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 72480 \, x - 242}{31250 \, {\left (5 \, x + 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 41, normalized size = 0.85 \begin {gather*} \frac {27 x^{4}}{25} - \frac {36 x^{3}}{125} - \frac {1449 x^{2}}{1250} + \frac {2416 x}{3125} + \frac {209 \log {\left (5 x + 3 \right )}}{3125} - \frac {121}{78125 x + 46875} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.32, size = 66, normalized size = 1.38 \begin {gather*} -\frac {1}{31250} \, {\left (5 \, x + 3\right )}^{4} {\left (\frac {720}{5 \, x + 3} - \frac {2115}{{\left (5 \, x + 3\right )}^{2}} - \frac {5750}{{\left (5 \, x + 3\right )}^{3}} - 54\right )} - \frac {121}{15625 \, {\left (5 \, x + 3\right )}} - \frac {209}{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 = 34, normalized size = 0.71 \begin {gather*} \frac {2416\,x}{3125}+\frac {209\,\ln \left (x+\frac {3}{5}\right )}{3125}-\frac {121}{78125\,\left (x+\frac {3}{5}\right )}-\frac {1449\,x^2}{1250}-\frac {36\,x^3}{125}+\frac {27\,x^4}{25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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