Optimal. Leaf size=76 \[ \frac {1}{105 (2+3 x)^5}-\frac {11}{196 (2+3 x)^4}-\frac {22}{1029 (2+3 x)^3}-\frac {22}{2401 (2+3 x)^2}-\frac {88}{16807 (2+3 x)}-\frac {176 \log (1-2 x)}{117649}+\frac {176 \log (2+3 x)}{117649} \]
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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 {88}{16807 (3 x+2)}-\frac {22}{2401 (3 x+2)^2}-\frac {22}{1029 (3 x+2)^3}-\frac {11}{196 (3 x+2)^4}+\frac {1}{105 (3 x+2)^5}-\frac {176 \log (1-2 x)}{117649}+\frac {176 \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) (2+3 x)^6} \, dx &=\int \left (-\frac {352}{117649 (-1+2 x)}-\frac {1}{7 (2+3 x)^6}+\frac {33}{49 (2+3 x)^5}+\frac {66}{343 (2+3 x)^4}+\frac {132}{2401 (2+3 x)^3}+\frac {264}{16807 (2+3 x)^2}+\frac {528}{117649 (2+3 x)}\right ) \, dx\\ &=\frac {1}{105 (2+3 x)^5}-\frac {11}{196 (2+3 x)^4}-\frac {22}{1029 (2+3 x)^3}-\frac {22}{2401 (2+3 x)^2}-\frac {88}{16807 (2+3 x)}-\frac {176 \log (1-2 x)}{117649}+\frac {176 \log (2+3 x)}{117649}\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 50, normalized size = 0.66 \begin {gather*} \frac {-\frac {7 \left (348226+1268025 x+1833480 x^2+1389960 x^3+427680 x^4\right )}{(2+3 x)^5}-10560 \log (3-6 x)+10560 \log (2+3 x)}{7058940} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 63, normalized size = 0.83
method | result | size |
risch | \(\frac {-\frac {7128}{16807} x^{4}-\frac {23166}{16807} x^{3}-\frac {30558}{16807} x^{2}-\frac {84535}{67228} x -\frac {174113}{504210}}{\left (2+3 x \right )^{5}}-\frac {176 \ln \left (-1+2 x \right )}{117649}+\frac {176 \ln \left (2+3 x \right )}{117649}\) | \(47\) |
norman | \(\frac {\frac {44789}{33614} x +\frac {400107}{67228} x^{2}+\frac {1381689}{134456} x^{3}+\frac {14103153}{5378240} x^{5}+\frac {4472955}{537824} x^{4}}{\left (2+3 x \right )^{5}}-\frac {176 \ln \left (-1+2 x \right )}{117649}+\frac {176 \ln \left (2+3 x \right )}{117649}\) | \(50\) |
default | \(-\frac {176 \ln \left (-1+2 x \right )}{117649}+\frac {1}{105 \left (2+3 x \right )^{5}}-\frac {11}{196 \left (2+3 x \right )^{4}}-\frac {22}{1029 \left (2+3 x \right )^{3}}-\frac {22}{2401 \left (2+3 x \right )^{2}}-\frac {88}{16807 \left (2+3 x \right )}+\frac {176 \ln \left (2+3 x \right )}{117649}\) | \(63\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.33, size = 66, normalized size = 0.87 \begin {gather*} -\frac {427680 \, x^{4} + 1389960 \, x^{3} + 1833480 \, x^{2} + 1268025 \, x + 348226}{1008420 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} + \frac {176}{117649} \, \log \left (3 \, x + 2\right ) - \frac {176}{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 = 1.25, size = 115, normalized size = 1.51 \begin {gather*} -\frac {2993760 \, x^{4} + 9729720 \, x^{3} + 12834360 \, x^{2} - 10560 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (3 \, x + 2\right ) + 10560 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (2 \, x - 1\right ) + 8876175 \, x + 2437582}{7058940 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\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 {427680 x^{4} + 1389960 x^{3} + 1833480 x^{2} + 1268025 x + 348226}{245046060 x^{5} + 816820200 x^{4} + 1089093600 x^{3} + 726062400 x^{2} + 242020800 x + 32269440} - \frac {176 \log {\left (x - \frac {1}{2} \right )}}{117649} + \frac {176 \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 = 0.53, size = 48, normalized size = 0.63 \begin {gather*} -\frac {427680 \, x^{4} + 1389960 \, x^{3} + 1833480 \, x^{2} + 1268025 \, x + 348226}{1008420 \, {\left (3 \, x + 2\right )}^{5}} + \frac {176}{117649} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {176}{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 = 1.12, size = 56, normalized size = 0.74 \begin {gather*} \frac {352\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{117649}-\frac {\frac {88\,x^4}{50421}+\frac {286\,x^3}{50421}+\frac {10186\,x^2}{1361367}+\frac {84535\,x}{16336404}+\frac {174113}{122523030}}{x^5+\frac {10\,x^4}{3}+\frac {40\,x^3}{9}+\frac {80\,x^2}{27}+\frac {80\,x}{81}+\frac {32}{243}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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