Optimal. Leaf size=76 \[ \frac {22}{2401 (1-2 x)^2}+\frac {388}{16807 (1-2 x)}+\frac {1}{343 (2+3 x)^3}-\frac {87}{4802 (2+3 x)^2}-\frac {558}{16807 (2+3 x)}-\frac {2280 \log (1-2 x)}{117649}+\frac {2280 \log (2+3 x)}{117649} \]
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Rubi [A]
time = 0.02, antiderivative size = 76, 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 {388}{16807 (1-2 x)}-\frac {558}{16807 (3 x+2)}+\frac {22}{2401 (1-2 x)^2}-\frac {87}{4802 (3 x+2)^2}+\frac {1}{343 (3 x+2)^3}-\frac {2280 \log (1-2 x)}{117649}+\frac {2280 \log (3 x+2)}{117649} \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int \frac {3+5 x}{(1-2 x)^3 (2+3 x)^4} \, dx &=\int \left (-\frac {88}{2401 (-1+2 x)^3}+\frac {776}{16807 (-1+2 x)^2}-\frac {4560}{117649 (-1+2 x)}-\frac {9}{343 (2+3 x)^4}+\frac {261}{2401 (2+3 x)^3}+\frac {1674}{16807 (2+3 x)^2}+\frac {6840}{117649 (2+3 x)}\right ) \, dx\\ &=\frac {22}{2401 (1-2 x)^2}+\frac {388}{16807 (1-2 x)}+\frac {1}{343 (2+3 x)^3}-\frac {87}{4802 (2+3 x)^2}-\frac {558}{16807 (2+3 x)}-\frac {2280 \log (1-2 x)}{117649}+\frac {2280 \log (2+3 x)}{117649}\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 57, normalized size = 0.75 \begin {gather*} \frac {-\frac {7 \left (-3088-33725 x-31160 x^2+75240 x^3+82080 x^4\right )}{(1-2 x)^2 (2+3 x)^3}-4560 \log (3-6 x)+4560 \log (2+3 x)}{235298} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 63, normalized size = 0.83
method | result | size |
risch | \(\frac {-\frac {41040}{16807} x^{4}-\frac {37620}{16807} x^{3}+\frac {15580}{16807} x^{2}+\frac {33725}{33614} x +\frac {1544}{16807}}{\left (-1+2 x \right )^{2} \left (2+3 x \right )^{3}}-\frac {2280 \ln \left (-1+2 x \right )}{117649}+\frac {2280 \ln \left (2+3 x \right )}{117649}\) | \(54\) |
norman | \(\frac {-\frac {992655}{33614} x^{4}-\frac {910575}{33614} x^{5}+\frac {1216665}{134456} x^{3}+\frac {1040345}{67228} x^{2}-\frac {32181}{16807}}{\left (-1+2 x \right )^{2} \left (2+3 x \right )^{3}}-\frac {2280 \ln \left (-1+2 x \right )}{117649}+\frac {2280 \ln \left (2+3 x \right )}{117649}\) | \(55\) |
default | \(\frac {22}{2401 \left (-1+2 x \right )^{2}}-\frac {388}{16807 \left (-1+2 x \right )}-\frac {2280 \ln \left (-1+2 x \right )}{117649}+\frac {1}{343 \left (2+3 x \right )^{3}}-\frac {87}{4802 \left (2+3 x \right )^{2}}-\frac {558}{16807 \left (2+3 x \right )}+\frac {2280 \ln \left (2+3 x \right )}{117649}\) | \(63\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 66, normalized size = 0.87 \begin {gather*} -\frac {82080 \, x^{4} + 75240 \, x^{3} - 31160 \, x^{2} - 33725 \, x - 3088}{33614 \, {\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )}} + \frac {2280}{117649} \, \log \left (3 \, x + 2\right ) - \frac {2280}{117649} \, \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 = 0.39, size = 115, normalized size = 1.51 \begin {gather*} -\frac {574560 \, x^{4} + 526680 \, x^{3} - 218120 \, x^{2} - 4560 \, {\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )} \log \left (3 \, x + 2\right ) + 4560 \, {\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )} \log \left (2 \, x - 1\right ) - 236075 \, x - 21616}{235298 \, {\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.09, size = 65, normalized size = 0.86 \begin {gather*} - \frac {82080 x^{4} + 75240 x^{3} - 31160 x^{2} - 33725 x - 3088}{3630312 x^{5} + 3630312 x^{4} - 1512630 x^{3} - 1949612 x^{2} + 134456 x + 268912} - \frac {2280 \log {\left (x - \frac {1}{2} \right )}}{117649} + \frac {2280 \log {\left (x + \frac {2}{3} \right )}}{117649} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.60, size = 55, normalized size = 0.72 \begin {gather*} -\frac {82080 \, x^{4} + 75240 \, x^{3} - 31160 \, x^{2} - 33725 \, x - 3088}{33614 \, {\left (3 \, x + 2\right )}^{3} {\left (2 \, x - 1\right )}^{2}} + \frac {2280}{117649} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {2280}{117649} \, \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 = 0.04, size = 53, normalized size = 0.70 \begin {gather*} \frac {4560\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{117649}+\frac {-\frac {380\,x^4}{16807}-\frac {1045\,x^3}{50421}+\frac {3895\,x^2}{453789}+\frac {33725\,x}{3630312}+\frac {386}{453789}}{x^5+x^4-\frac {5\,x^3}{12}-\frac {29\,x^2}{54}+\frac {x}{27}+\frac {2}{27}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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