Optimal. Leaf size=87 \[ \frac{5324}{117649 (1-2 x)}-\frac{14520}{117649 (3 x+2)}-\frac{3267}{33614 (3 x+2)^2}+\frac{121}{2401 (3 x+2)^3}-\frac{101}{12348 (3 x+2)^4}+\frac{1}{2205 (3 x+2)^5}-\frac{45012 \log (1-2 x)}{823543}+\frac{45012 \log (3 x+2)}{823543} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0422226, antiderivative size = 87, 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} \[ \frac{5324}{117649 (1-2 x)}-\frac{14520}{117649 (3 x+2)}-\frac{3267}{33614 (3 x+2)^2}+\frac{121}{2401 (3 x+2)^3}-\frac{101}{12348 (3 x+2)^4}+\frac{1}{2205 (3 x+2)^5}-\frac{45012 \log (1-2 x)}{823543}+\frac{45012 \log (3 x+2)}{823543} \]
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)^6} \, dx &=\int \left (\frac{10648}{117649 (-1+2 x)^2}-\frac{90024}{823543 (-1+2 x)}-\frac{1}{147 (2+3 x)^6}+\frac{101}{1029 (2+3 x)^5}-\frac{1089}{2401 (2+3 x)^4}+\frac{9801}{16807 (2+3 x)^3}+\frac{43560}{117649 (2+3 x)^2}+\frac{135036}{823543 (2+3 x)}\right ) \, dx\\ &=\frac{5324}{117649 (1-2 x)}+\frac{1}{2205 (2+3 x)^5}-\frac{101}{12348 (2+3 x)^4}+\frac{121}{2401 (2+3 x)^3}-\frac{3267}{33614 (2+3 x)^2}-\frac{14520}{117649 (2+3 x)}-\frac{45012 \log (1-2 x)}{823543}+\frac{45012 \log (2+3 x)}{823543}\\ \end{align*}
Mathematica [A] time = 0.0595437, size = 64, normalized size = 0.74 \[ \frac{2 \left (-\frac{7 \left (656274960 x^5+1804756140 x^4+1747028250 x^3+649342770 x^2+25985087 x-23684986\right )}{8 (2 x-1) (3 x+2)^5}-1012770 \log (1-2 x)+1012770 \log (6 x+4)\right )}{37059435} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.01, size = 72, normalized size = 0.8 \begin{align*} -{\frac{5324}{235298\,x-117649}}-{\frac{45012\,\ln \left ( 2\,x-1 \right ) }{823543}}+{\frac{1}{2205\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{101}{12348\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{121}{2401\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{3267}{33614\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{14520}{235298+352947\,x}}+{\frac{45012\,\ln \left ( 2+3\,x \right ) }{823543}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.2992, size = 103, normalized size = 1.18 \begin{align*} -\frac{656274960 \, x^{5} + 1804756140 \, x^{4} + 1747028250 \, x^{3} + 649342770 \, x^{2} + 25985087 \, x - 23684986}{21176820 \,{\left (486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right )}} + \frac{45012}{823543} \, \log \left (3 \, x + 2\right ) - \frac{45012}{823543} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.3636, size = 474, normalized size = 5.45 \begin{align*} -\frac{4593924720 \, x^{5} + 12633292980 \, x^{4} + 12229197750 \, x^{3} + 4545399390 \, x^{2} - 8102160 \,{\left (486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right )} \log \left (3 \, x + 2\right ) + 8102160 \,{\left (486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right )} \log \left (2 \, x - 1\right ) + 181895609 \, x - 165794902}{148237740 \,{\left (486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.19444, size = 75, normalized size = 0.86 \begin{align*} - \frac{656274960 x^{5} + 1804756140 x^{4} + 1747028250 x^{3} + 649342770 x^{2} + 25985087 x - 23684986}{10291934520 x^{6} + 29160481140 x^{5} + 28588707000 x^{4} + 7623655200 x^{3} - 5082436800 x^{2} - 3727120320 x - 677658240} - \frac{45012 \log{\left (x - \frac{1}{2} \right )}}{823543} + \frac{45012 \log{\left (x + \frac{2}{3} \right )}}{823543} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.85396, size = 105, normalized size = 1.21 \begin{align*} -\frac{5324}{117649 \,{\left (2 \, x - 1\right )}} + \frac{2 \,{\left (\frac{204418935}{2 \, x - 1} + \frac{740244225}{{\left (2 \, x - 1\right )}^{2}} + \frac{1185622375}{{\left (2 \, x - 1\right )}^{3}} + \frac{709135350}{{\left (2 \, x - 1\right )}^{4}} + 21049983\right )}}{4117715 \,{\left (\frac{7}{2 \, x - 1} + 3\right )}^{5}} + \frac{45012}{823543} \, \log \left ({\left | -\frac{7}{2 \, x - 1} - 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]