Optimal. Leaf size=87 \[ \frac {1}{126 (2+3 x)^6}-\frac {11}{245 (2+3 x)^5}-\frac {11}{686 (2+3 x)^4}-\frac {44}{7203 (2+3 x)^3}-\frac {44}{16807 (2+3 x)^2}-\frac {176}{117649 (2+3 x)}-\frac {352 \log (1-2 x)}{823543}+\frac {352 \log (2+3 x)}{823543} \]
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Rubi [A]
time = 0.02, antiderivative size = 87, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78}
\begin {gather*} -\frac {176}{117649 (3 x+2)}-\frac {44}{16807 (3 x+2)^2}-\frac {44}{7203 (3 x+2)^3}-\frac {11}{686 (3 x+2)^4}-\frac {11}{245 (3 x+2)^5}+\frac {1}{126 (3 x+2)^6}-\frac {352 \log (1-2 x)}{823543}+\frac {352 \log (3 x+2)}{823543} \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int \frac {3+5 x}{(1-2 x) (2+3 x)^7} \, dx &=\int \left (-\frac {704}{823543 (-1+2 x)}-\frac {1}{7 (2+3 x)^7}+\frac {33}{49 (2+3 x)^6}+\frac {66}{343 (2+3 x)^5}+\frac {132}{2401 (2+3 x)^4}+\frac {264}{16807 (2+3 x)^3}+\frac {528}{117649 (2+3 x)^2}+\frac {1056}{823543 (2+3 x)}\right ) \, dx\\ &=\frac {1}{126 (2+3 x)^6}-\frac {11}{245 (2+3 x)^5}-\frac {11}{686 (2+3 x)^4}-\frac {44}{7203 (2+3 x)^3}-\frac {44}{16807 (2+3 x)^2}-\frac {176}{117649 (2+3 x)}-\frac {352 \log (1-2 x)}{823543}+\frac {352 \log (2+3 x)}{823543}\\ \end {align*}
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Mathematica [A]
time = 0.06, size = 55, normalized size = 0.63 \begin {gather*} \frac {-\frac {7 \left (3013741+12254814 x+22413105 x^2+24841080 x^3+15075720 x^4+3849120 x^5\right )}{(2+3 x)^6}-31680 \log (3-6 x)+31680 \log (2+3 x)}{74118870} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 72, normalized size = 0.83
method | result | size |
risch | \(\frac {-\frac {42768}{117649} x^{5}-\frac {167508}{117649} x^{4}-\frac {276012}{117649} x^{3}-\frac {498069}{235298} x^{2}-\frac {680823}{588245} x -\frac {3013741}{10588410}}{\left (2+3 x \right )^{6}}-\frac {352 \ln \left (-1+2 x \right )}{823543}+\frac {352 \ln \left (2+3 x \right )}{823543}\) | \(52\) |
norman | \(\frac {\frac {330419}{235298} x +\frac {7937175}{470596} x^{3}+\frac {7048947}{941192} x^{2}+\frac {237270141}{18823840} x^{5}+\frac {244113021}{75295360} x^{6}+\frac {76010751}{3764768} x^{4}}{\left (2+3 x \right )^{6}}-\frac {352 \ln \left (-1+2 x \right )}{823543}+\frac {352 \ln \left (2+3 x \right )}{823543}\) | \(55\) |
default | \(-\frac {352 \ln \left (-1+2 x \right )}{823543}+\frac {1}{126 \left (2+3 x \right )^{6}}-\frac {11}{245 \left (2+3 x \right )^{5}}-\frac {11}{686 \left (2+3 x \right )^{4}}-\frac {44}{7203 \left (2+3 x \right )^{3}}-\frac {44}{16807 \left (2+3 x \right )^{2}}-\frac {176}{117649 \left (2+3 x \right )}+\frac {352 \ln \left (2+3 x \right )}{823543}\) | \(72\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 76, normalized size = 0.87 \begin {gather*} -\frac {3849120 \, x^{5} + 15075720 \, x^{4} + 24841080 \, x^{3} + 22413105 \, x^{2} + 12254814 \, x + 3013741}{10588410 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} + \frac {352}{823543} \, \log \left (3 \, x + 2\right ) - \frac {352}{823543} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.99, size = 135, normalized size = 1.55 \begin {gather*} -\frac {26943840 \, x^{5} + 105530040 \, x^{4} + 173887560 \, x^{3} + 156891735 \, x^{2} - 31680 \, {\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 ) + 31680 \, {\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 ) + 85783698 \, x + 21096187}{74118870 \, {\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 = 0.08, size = 75, normalized size = 0.86 \begin {gather*} - \frac {3849120 x^{5} + 15075720 x^{4} + 24841080 x^{3} + 22413105 x^{2} + 12254814 x + 3013741}{7718950890 x^{6} + 30875803560 x^{5} + 51459672600 x^{4} + 45741931200 x^{3} + 22870965600 x^{2} + 6098924160 x + 677658240} - \frac {352 \log {\left (x - \frac {1}{2} \right )}}{823543} + \frac {352 \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 = 0.55, size = 53, normalized size = 0.61 \begin {gather*} -\frac {3849120 \, x^{5} + 15075720 \, x^{4} + 24841080 \, x^{3} + 22413105 \, x^{2} + 12254814 \, x + 3013741}{10588410 \, {\left (3 \, x + 2\right )}^{6}} + \frac {352}{823543} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {352}{823543} \, \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 = 66, normalized size = 0.76 \begin {gather*} \frac {704\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{823543}-\frac {\frac {176\,x^5}{352947}+\frac {2068\,x^4}{1058841}+\frac {30668\,x^3}{9529569}+\frac {6149\,x^2}{2117682}+\frac {75647\,x}{47647845}+\frac {3013741}{7718950890}}{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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