Optimal. Leaf size=65 \[ \frac {242}{2401 (1-2 x)}-\frac {1}{441 (2+3 x)^3}+\frac {11}{343 (2+3 x)^2}-\frac {319}{2401 (2+3 x)}-\frac {1364 \log (1-2 x)}{16807}+\frac {1364 \log (2+3 x)}{16807} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.02, antiderivative size = 65, 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 {242}{2401 (1-2 x)}-\frac {319}{2401 (3 x+2)}+\frac {11}{343 (3 x+2)^2}-\frac {1}{441 (3 x+2)^3}-\frac {1364 \log (1-2 x)}{16807}+\frac {1364 \log (3 x+2)}{16807} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 90
Rubi steps
\begin {align*} \int \frac {(3+5 x)^2}{(1-2 x)^2 (2+3 x)^4} \, dx &=\int \left (\frac {484}{2401 (-1+2 x)^2}-\frac {2728}{16807 (-1+2 x)}+\frac {1}{49 (2+3 x)^4}-\frac {66}{343 (2+3 x)^3}+\frac {957}{2401 (2+3 x)^2}+\frac {4092}{16807 (2+3 x)}\right ) \, dx\\ &=\frac {242}{2401 (1-2 x)}-\frac {1}{441 (2+3 x)^3}+\frac {11}{343 (2+3 x)^2}-\frac {319}{2401 (2+3 x)}-\frac {1364 \log (1-2 x)}{16807}+\frac {1364 \log (2+3 x)}{16807}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.04, size = 54, normalized size = 0.83 \begin {gather*} \frac {2 \left (-\frac {7 \left (7277+66329 x+156519 x^2+110484 x^3\right )}{2 (-1+2 x) (2+3 x)^3}-6138 \log (1-2 x)+6138 \log (4+6 x)\right )}{151263} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.10, size = 54, normalized size = 0.83
method | result | size |
risch | \(\frac {-\frac {12276}{2401} x^{3}-\frac {17391}{2401} x^{2}-\frac {66329}{21609} x -\frac {7277}{21609}}{\left (-1+2 x \right ) \left (2+3 x \right )^{3}}-\frac {1364 \ln \left (-1+2 x \right )}{16807}+\frac {1364 \ln \left (2+3 x \right )}{16807}\) | \(49\) |
norman | \(\frac {-\frac {163701}{19208} x^{3}-\frac {21831}{9604} x^{4}-\frac {76841}{9604} x^{2}-\frac {10697}{4802} x}{\left (-1+2 x \right ) \left (2+3 x \right )^{3}}-\frac {1364 \ln \left (-1+2 x \right )}{16807}+\frac {1364 \ln \left (2+3 x \right )}{16807}\) | \(52\) |
default | \(-\frac {242}{2401 \left (-1+2 x \right )}-\frac {1364 \ln \left (-1+2 x \right )}{16807}-\frac {1}{441 \left (2+3 x \right )^{3}}+\frac {11}{343 \left (2+3 x \right )^{2}}-\frac {319}{2401 \left (2+3 x \right )}+\frac {1364 \ln \left (2+3 x \right )}{16807}\) | \(54\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.28, size = 56, normalized size = 0.86 \begin {gather*} -\frac {110484 \, x^{3} + 156519 \, x^{2} + 66329 \, x + 7277}{21609 \, {\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )}} + \frac {1364}{16807} \, \log \left (3 \, x + 2\right ) - \frac {1364}{16807} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.96, size = 95, normalized size = 1.46 \begin {gather*} -\frac {773388 \, x^{3} + 1095633 \, x^{2} - 12276 \, {\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )} \log \left (3 \, x + 2\right ) + 12276 \, {\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )} \log \left (2 \, x - 1\right ) + 464303 \, x + 50939}{151263 \, {\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.07, size = 56, normalized size = 0.86 \begin {gather*} \frac {- 110484 x^{3} - 156519 x^{2} - 66329 x - 7277}{1166886 x^{4} + 1750329 x^{3} + 388962 x^{2} - 432180 x - 172872} - \frac {1364 \log {\left (x - \frac {1}{2} \right )}}{16807} + \frac {1364 \log {\left (x + \frac {2}{3} \right )}}{16807} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 1.60, size = 60, normalized size = 0.92 \begin {gather*} -\frac {242}{2401 \, {\left (2 \, x - 1\right )}} + \frac {2 \, {\left (\frac {36120}{2 \, x - 1} + \frac {40621}{{\left (2 \, x - 1\right )}^{2}} + 8031\right )}}{16807 \, {\left (\frac {7}{2 \, x - 1} + 3\right )}^{3}} + \frac {1364}{16807} \, \log \left ({\left | -\frac {7}{2 \, x - 1} - 3 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.05, size = 46, normalized size = 0.71 \begin {gather*} \frac {2728\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{16807}-\frac {\frac {682\,x^3}{7203}+\frac {5797\,x^2}{43218}+\frac {66329\,x}{1166886}+\frac {7277}{1166886}}{x^4+\frac {3\,x^3}{2}+\frac {x^2}{3}-\frac {10\,x}{27}-\frac {4}{27}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________