Optimal. Leaf size=54 \[ \frac {1331}{686 (1-2 x)}-\frac {101}{3087 (3 x+2)}+\frac {1}{882 (3 x+2)^2}+\frac {363 \log (1-2 x)}{2401}-\frac {363 \log (3 x+2)}{2401} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 54, 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 = {88} \[ \frac {1331}{686 (1-2 x)}-\frac {101}{3087 (3 x+2)}+\frac {1}{882 (3 x+2)^2}+\frac {363 \log (1-2 x)}{2401}-\frac {363 \log (3 x+2)}{2401} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 88
Rubi steps
\begin {align*} \int \frac {(3+5 x)^3}{(1-2 x)^2 (2+3 x)^3} \, dx &=\int \left (\frac {1331}{343 (-1+2 x)^2}+\frac {726}{2401 (-1+2 x)}-\frac {1}{147 (2+3 x)^3}+\frac {101}{1029 (2+3 x)^2}-\frac {1089}{2401 (2+3 x)}\right ) \, dx\\ &=\frac {1331}{686 (1-2 x)}+\frac {1}{882 (2+3 x)^2}-\frac {101}{3087 (2+3 x)}+\frac {363 \log (1-2 x)}{2401}-\frac {363 \log (2+3 x)}{2401}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.05, size = 48, normalized size = 0.89 \[ \frac {\frac {83853}{1-2 x}-\frac {1414}{3 x+2}+\frac {49}{(3 x+2)^2}+6534 \log (1-2 x)-6534 \log (6 x+4)}{43218} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.53, size = 75, normalized size = 1.39 \[ -\frac {763161 \, x^{2} + 6534 \, {\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )} \log \left (3 \, x + 2\right ) - 6534 \, {\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )} \log \left (2 \, x - 1\right ) + 1007552 \, x + 332633}{43218 \, {\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.01, size = 51, normalized size = 0.94 \[ -\frac {1331}{686 \, {\left (2 \, x - 1\right )}} + \frac {2 \, {\left (\frac {231}{2 \, x - 1} + 100\right )}}{2401 \, {\left (\frac {7}{2 \, x - 1} + 3\right )}^{2}} - \frac {363}{2401} \, \log \left ({\left | -\frac {7}{2 \, x - 1} - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 45, normalized size = 0.83 \[ \frac {363 \ln \left (2 x -1\right )}{2401}-\frac {363 \ln \left (3 x +2\right )}{2401}+\frac {1}{882 \left (3 x +2\right )^{2}}-\frac {101}{3087 \left (3 x +2\right )}-\frac {1331}{686 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.50, size = 46, normalized size = 0.85 \[ -\frac {109023 \, x^{2} + 143936 \, x + 47519}{6174 \, {\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )}} - \frac {363}{2401} \, \log \left (3 \, x + 2\right ) + \frac {363}{2401} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.10, size = 37, normalized size = 0.69 \[ \frac {\frac {36341\,x^2}{37044}+\frac {35984\,x}{27783}+\frac {47519}{111132}}{-x^3-\frac {5\,x^2}{6}+\frac {2\,x}{9}+\frac {2}{9}}-\frac {726\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{2401} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.16, size = 46, normalized size = 0.85 \[ \frac {- 109023 x^{2} - 143936 x - 47519}{111132 x^{3} + 92610 x^{2} - 24696 x - 24696} + \frac {363 \log {\left (x - \frac {1}{2} \right )}}{2401} - \frac {363 \log {\left (x + \frac {2}{3} \right )}}{2401} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________