Optimal. Leaf size=97 \[ \frac {1}{14 (2+3 x)^6}+\frac {111}{245 (2+3 x)^5}+\frac {3897}{1372 (2+3 x)^4}+\frac {45473}{2401 (2+3 x)^3}+\frac {4774713}{33614 (2+3 x)^2}+\frac {167115051}{117649 (2+3 x)}-\frac {128 \log (1-2 x)}{9058973}-\frac {5849026977 \log (2+3 x)}{823543}+\frac {78125}{11} \log (3+5 x) \]
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Rubi [A]
time = 0.03, antiderivative size = 97, 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 = {84}
\begin {gather*} \frac {167115051}{117649 (3 x+2)}+\frac {4774713}{33614 (3 x+2)^2}+\frac {45473}{2401 (3 x+2)^3}+\frac {3897}{1372 (3 x+2)^4}+\frac {111}{245 (3 x+2)^5}+\frac {1}{14 (3 x+2)^6}-\frac {128 \log (1-2 x)}{9058973}-\frac {5849026977 \log (3 x+2)}{823543}+\frac {78125}{11} \log (5 x+3) \end {gather*}
Antiderivative was successfully verified.
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Rule 84
Rubi steps
\begin {align*} \int \frac {1}{(1-2 x) (2+3 x)^7 (3+5 x)} \, dx &=\int \left (-\frac {256}{9058973 (-1+2 x)}-\frac {9}{7 (2+3 x)^7}-\frac {333}{49 (2+3 x)^6}-\frac {11691}{343 (2+3 x)^5}-\frac {409257}{2401 (2+3 x)^4}-\frac {14324139}{16807 (2+3 x)^3}-\frac {501345153}{117649 (2+3 x)^2}-\frac {17547080931}{823543 (2+3 x)}+\frac {390625}{11 (3+5 x)}\right ) \, dx\\ &=\frac {1}{14 (2+3 x)^6}+\frac {111}{245 (2+3 x)^5}+\frac {3897}{1372 (2+3 x)^4}+\frac {45473}{2401 (2+3 x)^3}+\frac {4774713}{33614 (2+3 x)^2}+\frac {167115051}{117649 (2+3 x)}-\frac {128 \log (1-2 x)}{9058973}-\frac {5849026977 \log (2+3 x)}{823543}+\frac {78125}{11} \log (3+5 x)\\ \end {align*}
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Mathematica [A]
time = 0.04, size = 97, normalized size = 1.00 \begin {gather*} \frac {1}{14 (2+3 x)^6}+\frac {111}{245 (2+3 x)^5}+\frac {3897}{1372 (2+3 x)^4}+\frac {45473}{2401 (2+3 x)^3}+\frac {4774713}{33614 (2+3 x)^2}+\frac {167115051}{117649 (2+3 x)}-\frac {128 \log (1-2 x)}{9058973}-\frac {5849026977 \log (4+6 x)}{823543}+\frac {78125}{11} \log (6+10 x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 80, normalized size = 0.82
method | result | size |
risch | \(\frac {\frac {40608957393}{117649} x^{5}+\frac {273433644891}{235298} x^{4}+\frac {184154098887}{117649} x^{3}+\frac {496223395263}{470596} x^{2}+\frac {208981500498}{588245} x +\frac {56343426549}{1176490}}{\left (2+3 x \right )^{6}}-\frac {128 \ln \left (-1+2 x \right )}{9058973}-\frac {5849026977 \ln \left (2+3 x \right )}{823543}+\frac {78125 \ln \left (3+5 x \right )}{11}\) | \(60\) |
norman | \(\frac {-\frac {17825567589}{235298} x -\frac {784656121275}{470596} x^{3}-\frac {528825726297}{941192} x^{2}-\frac {34576924771341}{18823840} x^{5}-\frac {41074357954221}{75295360} x^{6}-\frac {9316514333151}{3764768} x^{4}}{\left (2+3 x \right )^{6}}-\frac {128 \ln \left (-1+2 x \right )}{9058973}-\frac {5849026977 \ln \left (2+3 x \right )}{823543}+\frac {78125 \ln \left (3+5 x \right )}{11}\) | \(63\) |
default | \(-\frac {128 \ln \left (-1+2 x \right )}{9058973}+\frac {1}{14 \left (2+3 x \right )^{6}}+\frac {111}{245 \left (2+3 x \right )^{5}}+\frac {3897}{1372 \left (2+3 x \right )^{4}}+\frac {45473}{2401 \left (2+3 x \right )^{3}}+\frac {4774713}{33614 \left (2+3 x \right )^{2}}+\frac {167115051}{117649 \left (2+3 x \right )}-\frac {5849026977 \ln \left (2+3 x \right )}{823543}+\frac {78125 \ln \left (3+5 x \right )}{11}\) | \(80\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 84, normalized size = 0.87 \begin {gather*} \frac {3 \, {\left (270726382620 \, x^{5} + 911445482970 \, x^{4} + 1227693992580 \, x^{3} + 827038992105 \, x^{2} + 278642000664 \, x + 37562284366\right )}}{2352980 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} + \frac {78125}{11} \, \log \left (5 \, x + 3\right ) - \frac {5849026977}{823543} \, \log \left (3 \, x + 2\right ) - \frac {128}{9058973} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 173 vs.
\(2 (79) = 158\).
time = 1.15, size = 173, normalized size = 1.78 \begin {gather*} \frac {62537794385220 \, x^{5} + 210543906566070 \, x^{4} + 283597312285980 \, x^{3} + 191046007176255 \, x^{2} + 1286785937500 \, {\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 ) - 1286785934940 \, {\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 ) - 2560 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )} \log \left (2 \, x - 1\right ) + 64366302153384 \, x + 8676887688546}{181179460 \, {\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 = 0.27, size = 87, normalized size = 0.90 \begin {gather*} - \frac {- 812179147860 x^{5} - 2734336448910 x^{4} - 3683081977740 x^{3} - 2481116976315 x^{2} - 835926001992 x - 112686853098}{1715322420 x^{6} + 6861289680 x^{5} + 11435482800 x^{4} + 10164873600 x^{3} + 5082436800 x^{2} + 1355316480 x + 150590720} - \frac {128 \log {\left (x - \frac {1}{2} \right )}}{9058973} + \frac {78125 \log {\left (x + \frac {3}{5} \right )}}{11} - \frac {5849026977 \log {\left (x + \frac {2}{3} \right )}}{823543} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.51, size = 62, normalized size = 0.64 \begin {gather*} \frac {3 \, {\left (270726382620 \, x^{5} + 911445482970 \, x^{4} + 1227693992580 \, x^{3} + 827038992105 \, x^{2} + 278642000664 \, x + 37562284366\right )}}{2352980 \, {\left (3 \, x + 2\right )}^{6}} + \frac {78125}{11} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {5849026977}{823543} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {128}{9058973} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.12, size = 75, normalized size = 0.77 \begin {gather*} \frac {78125\,\ln \left (x+\frac {3}{5}\right )}{11}-\frac {5849026977\,\ln \left (x+\frac {2}{3}\right )}{823543}-\frac {128\,\ln \left (x-\frac {1}{2}\right )}{9058973}+\frac {\frac {55705017\,x^5}{117649}+\frac {1125241337\,x^4}{705894}+\frac {6820522181\,x^3}{3176523}+\frac {18378644269\,x^2}{12706092}+\frac {7740055574\,x}{15882615}+\frac {18781142183}{285887070}}{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}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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