Optimal. Leaf size=76 \[ \frac {2662}{16807 (1-2 x)}+\frac {1}{1764 (2+3 x)^4}-\frac {101}{9261 (2+3 x)^3}+\frac {363}{4802 (2+3 x)^2}-\frac {3267}{16807 (2+3 x)}-\frac {14520 \log (1-2 x)}{117649}+\frac {14520 \log (2+3 x)}{117649} \]
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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 = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90}
\begin {gather*} \frac {2662}{16807 (1-2 x)}-\frac {3267}{16807 (3 x+2)}+\frac {363}{4802 (3 x+2)^2}-\frac {101}{9261 (3 x+2)^3}+\frac {1}{1764 (3 x+2)^4}-\frac {14520 \log (1-2 x)}{117649}+\frac {14520 \log (3 x+2)}{117649} \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)^2 (2+3 x)^5} \, dx &=\int \left (\frac {5324}{16807 (-1+2 x)^2}-\frac {29040}{117649 (-1+2 x)}-\frac {1}{147 (2+3 x)^5}+\frac {101}{1029 (2+3 x)^4}-\frac {1089}{2401 (2+3 x)^3}+\frac {9801}{16807 (2+3 x)^2}+\frac {43560}{117649 (2+3 x)}\right ) \, dx\\ &=\frac {2662}{16807 (1-2 x)}+\frac {1}{1764 (2+3 x)^4}-\frac {101}{9261 (2+3 x)^3}+\frac {363}{4802 (2+3 x)^2}-\frac {3267}{16807 (2+3 x)}-\frac {14520 \log (1-2 x)}{117649}+\frac {14520 \log (2+3 x)}{117649}\\ \end {align*}
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Mathematica [A]
time = 0.05, size = 59, normalized size = 0.78 \begin {gather*} \frac {2 \left (-\frac {7 \left (2287541+21109490 x+66510750 x^2+88209000 x^3+42340320 x^4\right )}{8 (-1+2 x) (2+3 x)^4}-196020 \log (1-2 x)+196020 \log (4+6 x)\right )}{3176523} \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 | \(\frac {-\frac {392040}{16807} x^{4}-\frac {816750}{16807} x^{3}-\frac {11085125}{302526} x^{2}-\frac {10554745}{907578} x -\frac {2287541}{1815156}}{\left (-1+2 x \right ) \left (2+3 x \right )^{4}}-\frac {14520 \ln \left (-1+2 x \right )}{117649}+\frac {14520 \ln \left (2+3 x \right )}{117649}\) | \(54\) |
norman | \(\frac {-\frac {221469}{33614} x -\frac {54828593}{1075648} x^{4}-\frac {6862623}{537824} x^{5}-\frac {8821541}{134456} x^{3}-\frac {4672551}{134456} x^{2}}{\left (-1+2 x \right ) \left (2+3 x \right )^{4}}-\frac {14520 \ln \left (-1+2 x \right )}{117649}+\frac {14520 \ln \left (2+3 x \right )}{117649}\) | \(57\) |
default | \(-\frac {2662}{16807 \left (-1+2 x \right )}-\frac {14520 \ln \left (-1+2 x \right )}{117649}+\frac {1}{1764 \left (2+3 x \right )^{4}}-\frac {101}{9261 \left (2+3 x \right )^{3}}+\frac {363}{4802 \left (2+3 x \right )^{2}}-\frac {3267}{16807 \left (2+3 x \right )}+\frac {14520 \ln \left (2+3 x \right )}{117649}\) | \(63\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 66, normalized size = 0.87 \begin {gather*} -\frac {42340320 \, x^{4} + 88209000 \, x^{3} + 66510750 \, x^{2} + 21109490 \, x + 2287541}{1815156 \, {\left (162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right )}} + \frac {14520}{117649} \, \log \left (3 \, x + 2\right ) - \frac {14520}{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 {296382240 \, x^{4} + 617463000 \, x^{3} + 465575250 \, x^{2} - 1568160 \, {\left (162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right )} \log \left (3 \, x + 2\right ) + 1568160 \, {\left (162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right )} \log \left (2 \, x - 1\right ) + 147766430 \, x + 16012787}{12706092 \, {\left (162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, 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 = 66, normalized size = 0.87 \begin {gather*} \frac {- 42340320 x^{4} - 88209000 x^{3} - 66510750 x^{2} - 21109490 x - 2287541}{294055272 x^{5} + 637119756 x^{4} + 392073696 x^{3} - 43563744 x^{2} - 116169984 x - 29042496} - \frac {14520 \log {\left (x - \frac {1}{2} \right )}}{117649} + \frac {14520 \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 = 0.59, size = 67, normalized size = 0.88 \begin {gather*} -\frac {3267}{16807 \, {\left (3 \, x + 2\right )}} + \frac {15972}{117649 \, {\left (\frac {7}{3 \, x + 2} - 2\right )}} + \frac {363}{4802 \, {\left (3 \, x + 2\right )}^{2}} - \frac {101}{9261 \, {\left (3 \, x + 2\right )}^{3}} + \frac {1}{1764 \, {\left (3 \, x + 2\right )}^{4}} - \frac {14520}{117649} \, \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 = 1.10, size = 57, normalized size = 0.75 \begin {gather*} \frac {29040\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{117649}+\frac {\frac {2420\,x^4}{16807}+\frac {15125\,x^3}{50421}+\frac {11085125\,x^2}{49009212}+\frac {10554745\,x}{147027636}+\frac {2287541}{294055272}}{-x^5-\frac {13\,x^4}{6}-\frac {4\,x^3}{3}+\frac {4\,x^2}{27}+\frac {32\,x}{81}+\frac {8}{81}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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