Optimal. Leaf size=68 \[ \frac{6934}{3 x+2}+\frac{7480}{5 x+3}+\frac{707}{2 (3 x+2)^2}-\frac{605}{2 (5 x+3)^2}+\frac{49}{3 (3 x+2)^3}-57110 \log (3 x+2)+57110 \log (5 x+3) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0323682, antiderivative size = 68, 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} \[ \frac{6934}{3 x+2}+\frac{7480}{5 x+3}+\frac{707}{2 (3 x+2)^2}-\frac{605}{2 (5 x+3)^2}+\frac{49}{3 (3 x+2)^3}-57110 \log (3 x+2)+57110 \log (5 x+3) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^2}{(2+3 x)^4 (3+5 x)^3} \, dx &=\int \left (-\frac{147}{(2+3 x)^4}-\frac{2121}{(2+3 x)^3}-\frac{20802}{(2+3 x)^2}-\frac{171330}{2+3 x}+\frac{3025}{(3+5 x)^3}-\frac{37400}{(3+5 x)^2}+\frac{285550}{3+5 x}\right ) \, dx\\ &=\frac{49}{3 (2+3 x)^3}+\frac{707}{2 (2+3 x)^2}+\frac{6934}{2+3 x}-\frac{605}{2 (3+5 x)^2}+\frac{7480}{3+5 x}-57110 \log (2+3 x)+57110 \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0456068, size = 70, normalized size = 1.03 \[ \frac{6934}{3 x+2}+\frac{7480}{5 x+3}+\frac{707}{2 (3 x+2)^2}-\frac{605}{2 (5 x+3)^2}+\frac{49}{3 (3 x+2)^3}-57110 \log (5 (3 x+2))+57110 \log (5 x+3) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.008, size = 63, normalized size = 0.9 \begin{align*}{\frac{49}{3\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{707}{2\, \left ( 2+3\,x \right ) ^{2}}}+6934\, \left ( 2+3\,x \right ) ^{-1}-{\frac{605}{2\, \left ( 3+5\,x \right ) ^{2}}}+7480\, \left ( 3+5\,x \right ) ^{-1}-57110\,\ln \left ( 2+3\,x \right ) +57110\,\ln \left ( 3+5\,x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.09595, size = 89, normalized size = 1.31 \begin{align*} \frac{15419700 \, x^{4} + 39577230 \, x^{3} + 38058104 \, x^{2} + 16250079 \, x + 2599404}{6 \,{\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )}} + 57110 \, \log \left (5 \, x + 3\right ) - 57110 \, \log \left (3 \, x + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.11943, size = 385, normalized size = 5.66 \begin{align*} \frac{15419700 \, x^{4} + 39577230 \, x^{3} + 38058104 \, x^{2} + 342660 \,{\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )} \log \left (5 \, x + 3\right ) - 342660 \,{\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )} \log \left (3 \, x + 2\right ) + 16250079 \, x + 2599404}{6 \,{\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.178922, size = 61, normalized size = 0.9 \begin{align*} \frac{15419700 x^{4} + 39577230 x^{3} + 38058104 x^{2} + 16250079 x + 2599404}{4050 x^{5} + 12960 x^{4} + 16578 x^{3} + 10596 x^{2} + 3384 x + 432} + 57110 \log{\left (x + \frac{3}{5} \right )} - 57110 \log{\left (x + \frac{2}{3} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 2.15399, size = 74, normalized size = 1.09 \begin{align*} \frac{15419700 \, x^{4} + 39577230 \, x^{3} + 38058104 \, x^{2} + 16250079 \, x + 2599404}{6 \,{\left (5 \, x + 3\right )}^{2}{\left (3 \, x + 2\right )}^{3}} + 57110 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 57110 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]