Optimal. Leaf size=55 \[ \frac {16807}{704 (1-2 x)^2}-\frac {156065}{1936 (1-2 x)}-\frac {10287 x}{400}-\frac {243 x^2}{80}-\frac {543655 \log (1-2 x)}{10648}+\frac {\log (3+5 x)}{166375} \]
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Rubi [A]
time = 0.02, antiderivative size = 55, 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 {243 x^2}{80}-\frac {10287 x}{400}-\frac {156065}{1936 (1-2 x)}+\frac {16807}{704 (1-2 x)^2}-\frac {543655 \log (1-2 x)}{10648}+\frac {\log (5 x+3)}{166375} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(2+3 x)^5}{(1-2 x)^3 (3+5 x)} \, dx &=\int \left (-\frac {10287}{400}-\frac {243 x}{40}-\frac {16807}{176 (-1+2 x)^3}-\frac {156065}{968 (-1+2 x)^2}-\frac {543655}{5324 (-1+2 x)}+\frac {1}{33275 (3+5 x)}\right ) \, dx\\ &=\frac {16807}{704 (1-2 x)^2}-\frac {156065}{1936 (1-2 x)}-\frac {10287 x}{400}-\frac {243 x^2}{80}-\frac {543655 \log (1-2 x)}{10648}+\frac {\log (3+5 x)}{166375}\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 55, normalized size = 1.00 \begin {gather*} \frac {\frac {254205875}{(1-2 x)^2}+\frac {858357500}{-1+2 x}-47005596 (3+5 x)-1293732 (3+5 x)^2-543655000 \log (5-10 x)+64 \log (3+5 x)}{10648000} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.13, size = 44, normalized size = 0.80
method | result | size |
risch | \(-\frac {243 x^{2}}{80}-\frac {10287 x}{400}+\frac {\frac {156065 x}{968}-\frac {439383}{7744}}{\left (-1+2 x \right )^{2}}-\frac {543655 \ln \left (-1+2 x \right )}{10648}+\frac {\ln \left (3+5 x \right )}{166375}\) | \(40\) |
default | \(-\frac {243 x^{2}}{80}-\frac {10287 x}{400}+\frac {16807}{704 \left (-1+2 x \right )^{2}}+\frac {156065}{1936 \left (-1+2 x \right )}-\frac {543655 \ln \left (-1+2 x \right )}{10648}+\frac {\ln \left (3+5 x \right )}{166375}\) | \(44\) |
norman | \(\frac {-\frac {1106513}{12100} x +\frac {3954117}{12100} x^{2}-\frac {2268}{25} x^{3}-\frac {243}{20} x^{4}}{\left (-1+2 x \right )^{2}}-\frac {543655 \ln \left (-1+2 x \right )}{10648}+\frac {\ln \left (3+5 x \right )}{166375}\) | \(45\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 44, normalized size = 0.80 \begin {gather*} -\frac {243}{80} \, x^{2} - \frac {10287}{400} \, x + \frac {2401 \, {\left (520 \, x - 183\right )}}{7744 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} + \frac {1}{166375} \, \log \left (5 \, x + 3\right ) - \frac {543655}{10648} \, \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 = 0.45, size = 70, normalized size = 1.27 \begin {gather*} -\frac {129373200 \, x^{4} + 965986560 \, x^{3} - 1063016460 \, x^{2} - 64 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (5 \, x + 3\right ) + 543655000 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 1442875060 \, x + 604151625}{10648000 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 44, normalized size = 0.80 \begin {gather*} - \frac {243 x^{2}}{80} - \frac {10287 x}{400} - \frac {439383 - 1248520 x}{30976 x^{2} - 30976 x + 7744} - \frac {543655 \log {\left (x - \frac {1}{2} \right )}}{10648} + \frac {\log {\left (x + \frac {3}{5} \right )}}{166375} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.50, size = 41, normalized size = 0.75 \begin {gather*} -\frac {243}{80} \, x^{2} - \frac {10287}{400} \, x + \frac {2401 \, {\left (520 \, x - 183\right )}}{7744 \, {\left (2 \, x - 1\right )}^{2}} + \frac {1}{166375} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {543655}{10648} \, \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 = 37, normalized size = 0.67 \begin {gather*} \frac {\ln \left (x+\frac {3}{5}\right )}{166375}-\frac {543655\,\ln \left (x-\frac {1}{2}\right )}{10648}-\frac {10287\,x}{400}+\frac {\frac {156065\,x}{3872}-\frac {439383}{30976}}{x^2-x+\frac {1}{4}}-\frac {243\,x^2}{80} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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