Optimal. Leaf size=81 \[ \frac {49}{54 (2+3 x)^6}+\frac {217}{45 (2+3 x)^5}+\frac {121}{4 (2+3 x)^4}+\frac {605}{3 (2+3 x)^3}+\frac {3025}{2 (2+3 x)^2}+\frac {15125}{2+3 x}-75625 \log (2+3 x)+75625 \log (3+5 x) \]
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Rubi [A]
time = 0.02, antiderivative size = 81, 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 {15125}{3 x+2}+\frac {3025}{2 (3 x+2)^2}+\frac {605}{3 (3 x+2)^3}+\frac {121}{4 (3 x+2)^4}+\frac {217}{45 (3 x+2)^5}+\frac {49}{54 (3 x+2)^6}-75625 \log (3 x+2)+75625 \log (5 x+3) \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)^7 (3+5 x)} \, dx &=\int \left (-\frac {49}{3 (2+3 x)^7}-\frac {217}{3 (2+3 x)^6}-\frac {363}{(2+3 x)^5}-\frac {1815}{(2+3 x)^4}-\frac {9075}{(2+3 x)^3}-\frac {45375}{(2+3 x)^2}-\frac {226875}{2+3 x}+\frac {378125}{3+5 x}\right ) \, dx\\ &=\frac {49}{54 (2+3 x)^6}+\frac {217}{45 (2+3 x)^5}+\frac {121}{4 (2+3 x)^4}+\frac {605}{3 (2+3 x)^3}+\frac {3025}{2 (2+3 x)^2}+\frac {15125}{2+3 x}-75625 \log (2+3 x)+75625 \log (3+5 x)\\ \end {align*}
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Mathematica [A]
time = 0.06, size = 55, normalized size = 0.68 \begin {gather*} \frac {275370238+2042732232 x+6063045615 x^2+9000258300 x^3+6681831750 x^4+1984702500 x^5}{540 (2+3 x)^6}-75625 \log (5 (2+3 x))+75625 \log (3+5 x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 72, normalized size = 0.89
method | result | size |
risch | \(\frac {3675375 x^{5}+\frac {24747525}{2} x^{4}+16667145 x^{3}+\frac {44911449}{4} x^{2}+\frac {56742562}{15} x +\frac {137685119}{270}}{\left (2+3 x \right )^{6}}-75625 \ln \left (2+3 x \right )+75625 \ln \left (3+5 x \right )\) | \(52\) |
norman | \(\frac {-\frac {1613333}{2} x -\frac {71016539}{4} x^{3}-\frac {47862221}{8} x^{2}-\frac {3129438213}{160} x^{5}-\frac {3717498213}{640} x^{6}-\frac {843205671}{32} x^{4}}{\left (2+3 x \right )^{6}}-75625 \ln \left (2+3 x \right )+75625 \ln \left (3+5 x \right )\) | \(55\) |
default | \(\frac {49}{54 \left (2+3 x \right )^{6}}+\frac {217}{45 \left (2+3 x \right )^{5}}+\frac {121}{4 \left (2+3 x \right )^{4}}+\frac {605}{3 \left (2+3 x \right )^{3}}+\frac {3025}{2 \left (2+3 x \right )^{2}}+\frac {15125}{2+3 x}-75625 \ln \left (2+3 x \right )+75625 \ln \left (3+5 x \right )\) | \(72\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 76, normalized size = 0.94 \begin {gather*} \frac {1984702500 \, x^{5} + 6681831750 \, x^{4} + 9000258300 \, x^{3} + 6063045615 \, x^{2} + 2042732232 \, x + 275370238}{540 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} + 75625 \, \log \left (5 \, x + 3\right ) - 75625 \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.48, size = 135, normalized size = 1.67 \begin {gather*} \frac {1984702500 \, x^{5} + 6681831750 \, x^{4} + 9000258300 \, x^{3} + 6063045615 \, x^{2} + 40837500 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )} \log \left (5 \, x + 3\right ) - 40837500 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )} \log \left (3 \, x + 2\right ) + 2042732232 \, x + 275370238}{540 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.19, size = 71, normalized size = 0.88 \begin {gather*} \frac {1984702500 x^{5} + 6681831750 x^{4} + 9000258300 x^{3} + 6063045615 x^{2} + 2042732232 x + 275370238}{393660 x^{6} + 1574640 x^{5} + 2624400 x^{4} + 2332800 x^{3} + 1166400 x^{2} + 311040 x + 34560} + 75625 \log {\left (x + \frac {3}{5} \right )} - 75625 \log {\left (x + \frac {2}{3} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.56, size = 53, normalized size = 0.65 \begin {gather*} \frac {1984702500 \, x^{5} + 6681831750 \, x^{4} + 9000258300 \, x^{3} + 6063045615 \, x^{2} + 2042732232 \, x + 275370238}{540 \, {\left (3 \, x + 2\right )}^{6}} + 75625 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 75625 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.10, size = 65, normalized size = 0.80 \begin {gather*} \frac {\frac {15125\,x^5}{3}+\frac {305525\,x^4}{18}+\frac {1851905\,x^3}{81}+\frac {1663387\,x^2}{108}+\frac {56742562\,x}{10935}+\frac {137685119}{196830}}{x^6+4\,x^5+\frac {20\,x^4}{3}+\frac {160\,x^3}{27}+\frac {80\,x^2}{27}+\frac {64\,x}{81}+\frac {64}{729}}-151250\,\mathrm {atanh}\left (30\,x+19\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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