Optimal. Leaf size=75 \[ \frac{16}{41503 (1-2 x)}-\frac{1998}{343 (3 x+2)}-\frac{625}{121 (5 x+3)}-\frac{27}{98 (3 x+2)^2}-\frac{2704 \log (1-2 x)}{3195731}+\frac{107109 \log (3 x+2)}{2401}-\frac{59375 \log (5 x+3)}{1331} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0387723, antiderivative size = 75, normalized size of antiderivative = 1., 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} \[ \frac{16}{41503 (1-2 x)}-\frac{1998}{343 (3 x+2)}-\frac{625}{121 (5 x+3)}-\frac{27}{98 (3 x+2)^2}-\frac{2704 \log (1-2 x)}{3195731}+\frac{107109 \log (3 x+2)}{2401}-\frac{59375 \log (5 x+3)}{1331} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 88
Rubi steps
\begin{align*} \int \frac{1}{(1-2 x)^2 (2+3 x)^3 (3+5 x)^2} \, dx &=\int \left (\frac{32}{41503 (-1+2 x)^2}-\frac{5408}{3195731 (-1+2 x)}+\frac{81}{49 (2+3 x)^3}+\frac{5994}{343 (2+3 x)^2}+\frac{321327}{2401 (2+3 x)}+\frac{3125}{121 (3+5 x)^2}-\frac{296875}{1331 (3+5 x)}\right ) \, dx\\ &=\frac{16}{41503 (1-2 x)}-\frac{27}{98 (2+3 x)^2}-\frac{1998}{343 (2+3 x)}-\frac{625}{121 (3+5 x)}-\frac{2704 \log (1-2 x)}{3195731}+\frac{107109 \log (2+3 x)}{2401}-\frac{59375 \log (3+5 x)}{1331}\\ \end{align*}
Mathematica [A] time = 0.067558, size = 65, normalized size = 0.87 \[ \frac{-\frac{77 \left (22224420 x^3+17783592 x^2-5074951 x-4684319\right )}{(3 x+2)^2 \left (10 x^2+x-3\right )}-5408 \log (3-6 x)+285124158 \log (3 x+2)-285118750 \log (-3 (5 x+3))}{6391462} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.01, size = 62, normalized size = 0.8 \begin{align*} -{\frac{16}{83006\,x-41503}}-{\frac{2704\,\ln \left ( 2\,x-1 \right ) }{3195731}}-{\frac{27}{98\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{1998}{686+1029\,x}}+{\frac{107109\,\ln \left ( 2+3\,x \right ) }{2401}}-{\frac{625}{363+605\,x}}-{\frac{59375\,\ln \left ( 3+5\,x \right ) }{1331}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.10372, size = 86, normalized size = 1.15 \begin{align*} -\frac{22224420 \, x^{3} + 17783592 \, x^{2} - 5074951 \, x - 4684319}{83006 \,{\left (90 \, x^{4} + 129 \, x^{3} + 25 \, x^{2} - 32 \, x - 12\right )}} - \frac{59375}{1331} \, \log \left (5 \, x + 3\right ) + \frac{107109}{2401} \, \log \left (3 \, x + 2\right ) - \frac{2704}{3195731} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] time = 1.53866, size = 408, normalized size = 5.44 \begin{align*} -\frac{1711280340 \, x^{3} + 1369336584 \, x^{2} + 285118750 \,{\left (90 \, x^{4} + 129 \, x^{3} + 25 \, x^{2} - 32 \, x - 12\right )} \log \left (5 \, x + 3\right ) - 285124158 \,{\left (90 \, x^{4} + 129 \, x^{3} + 25 \, x^{2} - 32 \, x - 12\right )} \log \left (3 \, x + 2\right ) + 5408 \,{\left (90 \, x^{4} + 129 \, x^{3} + 25 \, x^{2} - 32 \, x - 12\right )} \log \left (2 \, x - 1\right ) - 390771227 \, x - 360692563}{6391462 \,{\left (90 \, x^{4} + 129 \, x^{3} + 25 \, x^{2} - 32 \, x - 12\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.219854, size = 65, normalized size = 0.87 \begin{align*} - \frac{22224420 x^{3} + 17783592 x^{2} - 5074951 x - 4684319}{7470540 x^{4} + 10707774 x^{3} + 2075150 x^{2} - 2656192 x - 996072} - \frac{2704 \log{\left (x - \frac{1}{2} \right )}}{3195731} - \frac{59375 \log{\left (x + \frac{3}{5} \right )}}{1331} + \frac{107109 \log{\left (x + \frac{2}{3} \right )}}{2401} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 3.19763, size = 116, normalized size = 1.55 \begin{align*} -\frac{625}{121 \,{\left (5 \, x + 3\right )}} + \frac{5 \,{\left (\frac{604065417}{5 \, x + 3} + \frac{258530842}{{\left (5 \, x + 3\right )}^{2}} - 118375902\right )}}{913066 \,{\left (\frac{11}{5 \, x + 3} - 2\right )}{\left (\frac{1}{5 \, x + 3} + 3\right )}^{2}} + \frac{107109}{2401} \, \log \left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) - \frac{2704}{3195731} \, \log \left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]