Optimal. Leaf size=87 \[ \frac {1331}{16807 (1-2 x)^2}+\frac {14520}{117649 (1-2 x)}+\frac {1}{4116 (2+3 x)^4}-\frac {11}{2401 (2+3 x)^3}+\frac {1023}{33614 (2+3 x)^2}-\frac {7755}{117649 (2+3 x)}-\frac {59070 \log (1-2 x)}{823543}+\frac {59070 \log (2+3 x)}{823543} \]
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Rubi [A]
time = 0.03, antiderivative size = 87, 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 {14520}{117649 (1-2 x)}-\frac {7755}{117649 (3 x+2)}+\frac {1331}{16807 (1-2 x)^2}+\frac {1023}{33614 (3 x+2)^2}-\frac {11}{2401 (3 x+2)^3}+\frac {1}{4116 (3 x+2)^4}-\frac {59070 \log (1-2 x)}{823543}+\frac {59070 \log (3 x+2)}{823543} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(3+5 x)^3}{(1-2 x)^3 (2+3 x)^5} \, dx &=\int \left (-\frac {5324}{16807 (-1+2 x)^3}+\frac {29040}{117649 (-1+2 x)^2}-\frac {118140}{823543 (-1+2 x)}-\frac {1}{343 (2+3 x)^5}+\frac {99}{2401 (2+3 x)^4}-\frac {3069}{16807 (2+3 x)^3}+\frac {23265}{117649 (2+3 x)^2}+\frac {177210}{823543 (2+3 x)}\right ) \, dx\\ &=\frac {1331}{16807 (1-2 x)^2}+\frac {14520}{117649 (1-2 x)}+\frac {1}{4116 (2+3 x)^4}-\frac {11}{2401 (2+3 x)^3}+\frac {1023}{33614 (2+3 x)^2}-\frac {7755}{117649 (2+3 x)}-\frac {59070 \log (1-2 x)}{823543}+\frac {59070 \log (2+3 x)}{823543}\\ \end {align*}
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Mathematica [A]
time = 0.05, size = 64, normalized size = 0.74 \begin {gather*} \frac {-\frac {7 \left (-3991495-21371408 x-32767930 x^2+8860500 x^3+60605820 x^4+38277360 x^5\right )}{4 (1-2 x)^2 (2+3 x)^4}-177210 \log (1-2 x)+177210 \log (4+6 x)}{2470629} \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 | \(\frac {-\frac {3189780}{117649} x^{5}-\frac {5050485}{117649} x^{4}-\frac {738375}{117649} x^{3}+\frac {16383965}{705894} x^{2}+\frac {5342852}{352947} x +\frac {3991495}{1411788}}{\left (-1+2 x \right )^{2} \left (2+3 x \right )^{4}}-\frac {59070 \ln \left (-1+2 x \right )}{823543}+\frac {59070 \ln \left (2+3 x \right )}{823543}\) | \(59\) |
norman | \(\frac {-\frac {431001405}{7529536} x^{4}-\frac {230653755}{1882384} x^{5}-\frac {107770365}{1882384} x^{6}+\frac {37999445}{941192} x^{3}+\frac {2231403}{235298} x +\frac {39141765}{941192} x^{2}}{\left (-1+2 x \right )^{2} \left (2+3 x \right )^{4}}-\frac {59070 \ln \left (-1+2 x \right )}{823543}+\frac {59070 \ln \left (2+3 x \right )}{823543}\) | \(62\) |
default | \(\frac {1331}{16807 \left (-1+2 x \right )^{2}}-\frac {14520}{117649 \left (-1+2 x \right )}-\frac {59070 \ln \left (-1+2 x \right )}{823543}+\frac {1}{4116 \left (2+3 x \right )^{4}}-\frac {11}{2401 \left (2+3 x \right )^{3}}+\frac {1023}{33614 \left (2+3 x \right )^{2}}-\frac {7755}{117649 \left (2+3 x \right )}+\frac {59070 \ln \left (2+3 x \right )}{823543}\) | \(72\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 76, normalized size = 0.87 \begin {gather*} -\frac {38277360 \, x^{5} + 60605820 \, x^{4} + 8860500 \, x^{3} - 32767930 \, x^{2} - 21371408 \, x - 3991495}{1411788 \, {\left (324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right )}} + \frac {59070}{823543} \, \log \left (3 \, x + 2\right ) - \frac {59070}{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 = 0.42, size = 135, normalized size = 1.55 \begin {gather*} -\frac {267941520 \, x^{5} + 424240740 \, x^{4} + 62023500 \, x^{3} - 229375510 \, x^{2} - 708840 \, {\left (324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right )} \log \left (3 \, x + 2\right ) + 708840 \, {\left (324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right )} \log \left (2 \, x - 1\right ) - 149599856 \, x - 27940465}{9882516 \, {\left (324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.09, size = 75, normalized size = 0.86 \begin {gather*} - \frac {38277360 x^{5} + 60605820 x^{4} + 8860500 x^{3} - 32767930 x^{2} - 21371408 x - 3991495}{457419312 x^{6} + 762365520 x^{5} + 114354828 x^{4} - 372712032 x^{3} - 146825952 x^{2} + 45177216 x + 22588608} - \frac {59070 \log {\left (x - \frac {1}{2} \right )}}{823543} + \frac {59070 \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 = 1.88, size = 78, normalized size = 0.90 \begin {gather*} -\frac {7755}{117649 \, {\left (3 \, x + 2\right )}} + \frac {4356 \, {\left (\frac {217}{3 \, x + 2} - 51\right )}}{823543 \, {\left (\frac {7}{3 \, x + 2} - 2\right )}^{2}} + \frac {1023}{33614 \, {\left (3 \, x + 2\right )}^{2}} - \frac {11}{2401 \, {\left (3 \, x + 2\right )}^{3}} + \frac {1}{4116 \, {\left (3 \, x + 2\right )}^{4}} - \frac {59070}{823543} \, \log \left ({\left | -\frac {7}{3 \, x + 2} + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.09, size = 65, normalized size = 0.75 \begin {gather*} \frac {118140\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{823543}+\frac {-\frac {9845\,x^5}{117649}-\frac {187055\,x^4}{1411788}-\frac {246125\,x^3}{12706092}+\frac {16383965\,x^2}{228709656}+\frac {1335713\,x}{28588707}+\frac {3991495}{457419312}}{x^6+\frac {5\,x^5}{3}+\frac {x^4}{4}-\frac {22\,x^3}{27}-\frac {26\,x^2}{81}+\frac {8\,x}{81}+\frac {4}{81}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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