Optimal. Leaf size=54 \[ \frac {3469}{9261 (3 x+2)}-\frac {103}{2646 (3 x+2)^2}+\frac {1}{567 (3 x+2)^3}-\frac {1331 \log (1-2 x)}{2401}+\frac {1331 \log (3 x+2)}{2401} \]
[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} \[ \frac {3469}{9261 (3 x+2)}-\frac {103}{2646 (3 x+2)^2}+\frac {1}{567 (3 x+2)^3}-\frac {1331 \log (1-2 x)}{2401}+\frac {1331 \log (3 x+2)}{2401} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 88
Rubi steps
\begin {align*} \int \frac {(3+5 x)^3}{(1-2 x) (2+3 x)^4} \, dx &=\int \left (-\frac {2662}{2401 (-1+2 x)}-\frac {1}{63 (2+3 x)^4}+\frac {103}{441 (2+3 x)^3}-\frac {3469}{3087 (2+3 x)^2}+\frac {3993}{2401 (2+3 x)}\right ) \, dx\\ &=\frac {1}{567 (2+3 x)^3}-\frac {103}{2646 (2+3 x)^2}+\frac {3469}{9261 (2+3 x)}-\frac {1331 \log (1-2 x)}{2401}+\frac {1331 \log (2+3 x)}{2401}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.04, size = 40, normalized size = 0.74 \[ \frac {\frac {7 \left (187326 x^2+243279 x+79028\right )}{(3 x+2)^3}-215622 \log (1-2 x)+215622 \log (6 x+4)}{388962} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.88, size = 75, normalized size = 1.39 \[ \frac {1311282 \, x^{2} + 215622 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) - 215622 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (2 \, x - 1\right ) + 1702953 \, x + 553196}{388962 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.91, size = 38, normalized size = 0.70 \[ \frac {187326 \, x^{2} + 243279 \, x + 79028}{55566 \, {\left (3 \, x + 2\right )}^{3}} + \frac {1331}{2401} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {1331}{2401} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 45, normalized size = 0.83 \[ -\frac {1331 \ln \left (2 x -1\right )}{2401}+\frac {1331 \ln \left (3 x +2\right )}{2401}+\frac {1}{567 \left (3 x +2\right )^{3}}-\frac {103}{2646 \left (3 x +2\right )^{2}}+\frac {3469}{9261 \left (3 x +2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.60, size = 46, normalized size = 0.85 \[ \frac {187326 \, x^{2} + 243279 \, x + 79028}{55566 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + \frac {1331}{2401} \, \log \left (3 \, x + 2\right ) - \frac {1331}{2401} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.12, size = 35, normalized size = 0.65 \[ \frac {2662\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{2401}+\frac {\frac {3469\,x^2}{27783}+\frac {27031\,x}{166698}+\frac {39514}{750141}}{x^3+2\,x^2+\frac {4\,x}{3}+\frac {8}{27}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.17, size = 46, normalized size = 0.85 \[ - \frac {- 187326 x^{2} - 243279 x - 79028}{1500282 x^{3} + 3000564 x^{2} + 2000376 x + 444528} - \frac {1331 \log {\left (x - \frac {1}{2} \right )}}{2401} + \frac {1331 \log {\left (x + \frac {2}{3} \right )}}{2401} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________